Haven't played the game for some time, but I have beaten the game in legendary ironman multiple times. Anyways...
a veteran sniper misses a soldier (not in cover) 2 squares away,
If you look at the bottom left corner, their should be some information regarding how the to-hit possibility is calculated. If someone is that close to your sniper, you should notice that there would be a -15% debuff to your hit chance, which makes sniper terrible at close range. Personally, I almost never use dedicate sniper until mid-late game, because they are too immobile. They perform a lot better as gunslingers.
a grenade tears a wall off of a building but damages a robot for half the amount of an unupgraded basic pistol/rifle
Likely that the robot still has armor (rellow thingy next to the health bar). Armor will absorb damage but can be broken by explosions and certain weapons.
enemies hit me through walls, doesn't matter if my squad is in cover or not, they seem to hit almost all the time
while my soldiers miss even in the most ridiculous situations (like 1 square shotgun misses etc.), the hit accuracy
seems completely random
the experience so far has been very frustrating and I'm even playing on easy
One big advice: all your soldiers are expendable cannon fodder until mid game. Bad rolls happen all the time, this is life. Early game rookies don't have enough health to tank the shots. That said, there are ways to minimalize casualties and increase your chance of winning:
1. Kill as many enemies as you can before they can attack you. Always focus fire to kill enemies. Prioritize powerful enemies such as lancers, captains, or mechs if you can.
2. Increase your chance to hit by:
* Attacking enemies from closer range. For all non-sniper rifle weapons, your chance to hit increase as you get closer to enemies.
* Use grenade to destroy enemy's cover, especially in early game. I usually bring two grenadier in early missions. Grenades are far more reliable at this stage.
* Use the high ground. Being at a higher elevation improves your chance to hit by 15%. Be careful when using a building though, as grenades and other explosives can destroy the floor and the fall damage can easily kill your rookies.
* Flanking enemies. Note that you actually get extra to-hit bonus as you come closer to flanking an enemy, even if the enemy is still in cover.
3. Do the following:
* Position your troops behind high cover (identified by the full shield icon) as often as you can. High cover offers twice the protection of low cover
* Research magnetic weapon as early as you can. You need the extra oomph. Also,build Guerilla School as early as you can and buy squad size upgrade. Bigger squad = more guns = dead aliens.
* Treat rookies as grenadiers. They will miss most of their shots, so just let them throw grenades instead. Grenades never miss. While we're at it, grenadier is king in early game so train as many as you can.
* Your first ranger should learn phantom. This allows him to remain concealed and act as a forward scout. Being able to know what's ahead of you is invaluable.
* As your squads become more experienced, you should start to rotate your soldiers. Have 3 to 4 veterans lead 1 to 2 low rank soldiers. Aim for a 8-10 men A-team, and a B-team of equal size. So if your veterans have to stay in sick bad for two weeks, there will always be people to replace them.
4. Avoid the following:
* Reload the game when alien one-shot your best soldier through cover. It won't work. The quickest (but somewhat inaccurate) way to explain this is that the dice has been cast and if you reload, the game simply loads the same die (which has been cast so nothing changes).
* Melee. Unless you have a phantom ranger or reaper scouting ahead, the risk of revealing another alien patrol is too damn high.
* Bunching up. Many advent units carriers grenades. If all of your soldiers bunch together in one place, they will be easily destroyed by one grenade. Try to keep your soldiers 3 to 5 tiles away from each other.
* Customizing your rookies. All soldiers below sergeant rank are worthless cannon fodders.They should feel happy to die for mother Terra.
* Somke grenade. It's very bad. While we're at it. Flamethrower is also a terrible weapon.
5. Additional tips
* Flashbang is very useful in early game. It decreases enemy's aim and stops certain abilities, such as mind control from sectoid.
* You can lose a dozen missions and two dozen soldiers and still win the campaign. Don't be afraid to use the evac button to salvage a failing mission, especially if your most senior soldiers are in danger. Saving experienced soldier is more important than anything.
* Likewise, if you have the time, you can run away from enemies. Enemy AI is hilariously bad at chasing.
Hope this helps.