Do you have to be a high level for a bigger chance of winning a giveaway?

No, same for everyone.

higher lvl = less people entering = higher chance of winning basically

You have to be higher level to enter higher level giveaways.
Since there are fewer people at those higher levels, then yes, your odds of winning are much better.

You can enter more giveaways with a higher level

^^ More or less what everyone else has already said. Basically it helps to be a higher level since you will be able to actually enter better giveaways. The exceptions being the giveaways anyone can enter; the puzzle giveaways are a good place to look if you don't want to increase your level (usually the more challenging ones yield better results and are typically worth it imo). Of course its always nice for everyone else when others are giving away games and it helps to raise your level, as well as making entering giveaways - which are higher than your level - possible.

No, the "chance" is the same for everyone, no matter which level...but you can join more giveaways.