I'm an FTL beginner who just beat the game, and needed to learn 2 key behaviors:
1. Don't speed through sectors.
2. Rebel encounters look like instant death spreading across the sector, but are actually simply a low value combat.

I think a "practice" difficulty could be edited in with a key change to the rebel encounters:
1. The rebel wave never advances. The player has all the time they need, which encourages exploring.
2. The exit from a sector always has a rebel encounter, so the player learns to confront it rather than flee it.

Once a new player has practiced exploring (no time constraint), and the mystery is taken out of rebel encounters, the game becomes much more entertaining.

There is a mod available to disable the rebel fleet. At the beginning i was thinking running into the rebel fleet was instant death too so i used this mod for a few playthroughs. But when you are using this mod and get to the fourth or fifth sector every ship feels nearly the same since you have upgraded all necessary systems.

There is a practice mode. I think it's labelled as "Easy" in the game. ;)

Making fun of beginners is easier than helping people play the game, but it's not very constructive. The "rebels disabled" mod sounds like half the battle. That still leaves a beginner fleeing in terror from the rebel fleet.

I agree exploration and the advancing fleet are vital to the game. But how does a beginner learn not to run?

The game shows a menacing wave of red, which encourages fleeing at top speed. That's the lesson of the "easy" difficulty, to run. The beginner needs to be slowed down, and made to explore or their enjoyment will be doomed before they reach the final battle.

An alternative could be a tutorial that forces a fight with the rebel fleet. Maybe the player could start behind the rebel wave and be forced to run out in front of it.

I think most of the playtime in this game comes from trying over and over again. At least it was for me. If there was a tutorial that would explain that it is important to explore as much sectors as possible i think the playtime would be much shorter since if you manage to upgrade your ship to a certain degree it is easy to win almost every battle. At the beginning you always need a good portion of luck not to run into the wrong encounters. (Against a ship with combat drones when you try the Stealth Cruiser for example).
But as i said i was using a mod to disable the fleet since it was no fun for me to loose the game too often.

Agreed - I'm happy to help if you provide some specifics.

As to the specifics you've already provided: I tend to agree with most others here that learning to deal with the rebel fleet - that is, exploring as much as possible before they get to you - is an important skill to learn. Disabling the fleet (which you can do via a mod) would destroy the challenge. Also I think that disabling the fleet while learning the ropes (so to speak) wouldn't really be that beneficial for when you feel confident enough to turn it back on again - as you wouldn't have the practice of exploring as much as possible before they get to you.

I would think that the rebel fleet encounters are easier on the "easy" mode? If so, then having them catch up would provide some practice fighting them without them being overly difficult? I could be wrong on this, since I've played the game enough that rebel fleet encounters don't bother me even on normal (hell I've even had them catch up on purpose just for kicks on occasion).

From memory, the most difficult encounters for me when starting out was encountering something that my ship wasn't equipped for - e.g. automated ships with a ship not equipped to handle them, or a ship that just seems more powerful than mine due to me not upgrading enough at that point (or due to randomness).

I guess the biggest tips (which you may have heard before) would be:
1. Explore as much as possible without getting the fleet onto you.
2. Don't be afraid to run (power to engines and hold out, then GTFO of there!) if you're against something that's wiping the floor with you.

Point 2 is incidentally something I still screw up on every now and then. Even if you win such a battle, you could end up being so weakened that you spend your scrap on repairs instead of upgrades, which could hamper your game. The scrap you get in such a situation won't make up for the repair bill!

One final tip: see if you can get teleporters and board them as often as possible. Killing the crew by boarding (or via the anti-personnel beam - if you can get it!) nets you MUCH more scrap than destroying the ship.