The consequences of the wording of a wish are, as you note, entirely at the whim of a DM. No one can answer how any particular DM will rule, so keep in mind that any answer is on shaky ground, subjectively.
A DM could rule that you are granted this ability by virtue of being unable to cast Wish for anything but spell duplication, for example.
However, the wish you specify will have to be cast before it takes effect, and you could almost certainly undergo stress from it, with the potential of it being permanent.
I first want to know if a caster is bound to not be able to cast wish anymore, meaning that in the best case after 33 casts without suffering the stress, the caster will definitely suffer it on the 34th cast.
If the caster fails their "stress test" then yes, they are bound do not be able to cast wish anymore. But the "33 tries, then fail on the 34th" isn't how probability works. (This is; the short of it is that "best" case is that the stress test never fails, but that 70% of casters will experience that failure by their third casting.)
Second, I would like to know who or what decides that 33 percent is achieved. Does a dice have to be rolled? Must another random mechanism be used? And who triggers it: the DM or the player?
You are free to execute the mechanics of D&D however you like. Most people use dice as their random number generators. Many use high-quality computerized PRNGs that feature animations of dice in their readout. You can flip coins, draw cards, pebbles from an urn..., or anything that your group agrees upon. For standardization the authors assume everyone is using dice and they use dice notation to express quantities.
The player triggers it, by casting wish. Whether the player or the GM rolls (or otherwise initiates random number generation) is up to your table's conventions.
Finally, if the DM/player wants to roll, can the roll be a d6, or must it be a d100? The spell says "33.0" percent, right? Not 1/3 (or 33.333... percent). So a d6 can't be used, can't it?
The spell indeed says 33%, so you're right that "1-2 on a d6" isn't quite RAW. It's off by 1-in-300. Your table will have to decide whether that level of error is tolerable if someone wants to use a d6 (or d12, even!) in place of percentile dice.
Also, can feats, abilities or spells altering the roll be used?
It's going to depend on the feat/ability/spell. But it's almost certainly "no," given the wording of many of those abilities. Note that this roll isn't an attack, check, or save, which Halfling Luck or [dis]advantage would require. The Lucky feat or divination wizard's Portent require a d20 roll. Bless or bane or guidance... none of those would apply. The point being: the source of a die modification should tell you enough as to whether it'd apply to this roll.
Best Answer
Yeah, you would end up with a spell you can't cast. Fortunately, at level 17, you are not stuck with it forever, because:
So at level-up, you could drop Wish and replace it with something else. Once you hit 20th level though, if you still have it, you're pretty much stuck with it.
You could at that point ask your DM whether you could replace it as a down-time activity, though. It's not in the books but it seems reasonable that you don't get stuck with it for all eternity when a lesser Sorcerer would have a way to get rid of it...