The "oily" water tiles are impassible. There are some tiles that have stepping stones and you can cross these, also diagonal movement is possible to move between impassible tiles.

I found a pendant after walking on four oily tiles, chess horse movement like shape. I can also see two areas unexplored separated only by oily tiles but found no way to reach them and all baddies are now too strong for my next move. Again.

This isn't adding up. If you've gotten far enough in the tutorial to have found one of the pendants then you already have the fireball glyph, and that gives you enough firepower to beat almost any monster you'll encounter in the tutorial. Do you think you could post a screenshot so I can see where you are, because this isn't making sense to me.

I did not follow the tutorial, I just started and the caravan was assaulted and a lone security guard was in the dungeon. Lets face it, when you download games under accounts that can identify you and the games are patched, you are open to wind up with special versions specially for you no one will recognize are specially made for you. I have the impression my game is unbalanced, I ended several times with one less mana for the next item and one less exp point for next level and only the boss left to kill but not enough health nor new blocks to not suicide in the attempt. For the very first dungeon, this is very deterring. Since I purchased the game after playing out the nearest competitor which I caught in offer, I paid for it full price and have to play it, otherwise I would simply send it for later limbo. I did NOT want to follow the tutorial and was right, it feels like a slowed down spoiler... till I get to the same spot where I end dungeons with one mana less for next item and one exp point less for next level and... The puzzles are clearly unsolvable, also. So far only one worked out, the others rely on pure random and it seems it will never favor me. So! Do I send this game to the category of sabotaged games were the game could be very enjoyable but...? Or maybe a bona fide patch will address this issue and deliver a balanced game? I cannot send a screenshot, the game ended in a system crash after having it in wait for a few days.

Desktop Dungeons is special in that it's not a RPG, it's a puzzle game disguised as an RPG. Some dungeons, puzzles and challenges may seems impossible but as you keep playing, you pick up some new tricks, discovers some new interactions, combos and synergies between various powers, classes, races, items and game elements that allow you to break through walls that seemed impossible initially. And these seemingly impossible obstacles, the game has dozens more in store for you.

In a nutshell, it's like being given the numbers 2, 3, 5, 7, 11 and 13 and being told you need to add and subtract these numbers to get 33. And after you toil hard, you are told "nice, now combine these number to get 518" and you think "Whoa, this is impossible..." but then after much experimentation, you discover about multiplying and dividing, and solve the challenge only to be told "Ok, now get 15874" and then you think "Ok, this game's trolling me..." but you discover about power and square root... and the challenges keep ranking up and ranking up and the game constantly keeps you on your toes, forcing you to discover new sneaky mathematics magic tricks you didn't think were possible but were 100% intended by the developers.

It's not a RPG, it's not about killing weak monsters and linearly become stronger, it's about killing monsters that are ways stronger than you are and using the weak monsters as tools and resources to be used in order kill the big ones that will make you exponentially stronger, strong enough to defeat the boss.

The game hasn't been patched in months now, and the challenges and balance are in the same state as they were when I played the game this summer.

Without going into details on all the tricks and tactics you haven't discovered, I say, play the tutorial, read all the tool tips, and once you finish the tutorial, go straight away in the Explorer Guild in your kingdom to play the puzzle packs, as these will teach you tips, tricks and give you invaluable insights on how the devs expect you to play the game. I played those puzzle packs something like 50 hours into the game as a was getting stumped on the endgame challenges, and they still managed to teach me a trick or two. The whole game is like that, the whole game is about figuring out the tricks required to squeeze an extra exp point or one mana point necessary to complete a dungeon.

Now I adopted a new strategy: do as much as you can and leave the dungeon while still alive (...) and having money, otherwise I am just dying and dying and spending and spending and going nowhere because the dungeon turns impossible. I still think the game puzzle is not very well balanced so there is no guarantee any particular dungeon can be solved or any particular character can fill the role and finish a particular dungeon... without luck, that is, by playing with the random number generator till you get a favourable situation. The one mana less for activation, one point less for next level issue is particularly annoying even when you can use tricks sometimes to overcome the difference, because most times you only arrive at a dead end. This is a hard problem, the underlying generation of numbers may be faulty and will not provide a solution always, unlike, say, RPGs where statistics are inherently well balanced and not completely subjected to randomicity, or the game provides leveling mechanisms like drilling or accumulation of points to beat the game at the least maximum level should your character be way below opponent levels. Frankly, you would have to do statistical probabilities over random walks to generate or dynamically adapt dungeons to overcome the one point less problem, and I do not think the programmers are using those techniques...

Blueskirt42 and Syntotic gets it!
:)

There's a bunch of tricks you need to pick up.

There's a whole bunch of ways to gain bonus experience, killing monsters that are higher level than you is one way, but you can also use some glyphs to gain extra experience here and there. You can use the IMAWAL glyph to petrify enemies. Once a monster is petrified, you receive a buff that gives you 50% more experience on your next kill. Petrify level 1 monsters and use that buff to get more experience from stronger monsters. Petrify level 9 monsters to get more experience on from monsters that you are able to kill right now. The WEYTWUT and WONAFYT glyphs puts a Slowed debuff on monsters. That debuff lasts only one turn (once you attack the slowed monster, the debuff will be gone next turn) but if you kill a monster that has the Slowed debuff, you gain 1 bonus experience point. You can combine all those tricks on a single monster, to gain massive experience yield. But more importantly, start doing this as early as possible in order to avoid those situations where you are a stuck one experience short from leveling up.

Don't kill all the weak monsters you see. Every time you level up, you refill your health and mana. But if you leave weak monsters here and there, you can use them to level up in the middle of a bigger fight: if you only need one XP to level up, you can go attack a tough monster, and when you've used all your mana and health and you're about to die, you can go punch a weak, low level monster in order to instantly gain a level and refill your health and mana, and use that health and mana to deal the killing blow to that tough monster and get bonus experience.

It is uttermost important that you use those tricks to accelerate your level growth, because if you kill all the level 1 monsters, and then kill all the level 2 monsters, and then kill all level 3 monsters... in order, you will constantly find yourself stuck at level 6 and unable to defeat the stronger monsters. Right from the start, find a level 2 monsters that is easy to kill to get that bonus experience, when you're level 2, look for level 3 monsters that are easy to kill, when you are level 3, look for level 5 monsters that are easy to kill...

1 1 1 1 1 1 1 1,
You can play them like this:
1 + 1 + 1 + 1 +1 + 1 + 1 + 1 = 8
But you can also play them like this:
(1 + 1) x (1 + 1) x (1 + 1) x (1 + 1) = 16
Or like this:
(1 + 1 + 1) x (1 + 1 + 1) x (1 + 1) = 18

That's the way the game is played, it's all about using the gold, the items, the glyphs, the weak monsters, the strong monsters, the class abilities, the conversion bonus, the potions, the deities, the unexplored dungeon tiles... and combining them in the correct order, using them in the most efficient way possible, to get the biggest bang for your bucks to defeat the boss. And then finding new ways to use them, to defeat bigger ones.

Lots of useful tips from Blueskirt for you there, Syntotic. In a proper puzzle game like this, avoiding the tutorial just because you feel it is a type of slow spoiler, is not the best approach. Have you at least figured out the "convert" trick yet? That is a very important tool on some of the puzzles / dungeons.