Sometimes, but most cases are quite simple. I learned the difference between they're/there/their sometime before grade 8, and I generally expect people I converse with to recognize that distinction.
As for possessive forms - that's even easier. In most cases, if something belongs to someone, use an apostrophe. If it doesn't, then don't. Okay, it can get confusing, but in most cases, it's not.
I'm a native English speaker and my name ends in 's', yet even I waffle about whether I just use an apostrophe. I generally include an apostrophe just for consistency.
My heuristic is: if I would pronounce the extra sound, then include the apostrophe. Unfortunately, this would not help non-native speakers.. <:)
And yet if you try to trace back why those "rules" have any authority and you're likely to end-up back at a claim that it was what everyone did in their real life.
Conventionally, you would just say "Jesses" and the possessive would be clear from context.
As for the apostrophe, the veritable Strunk & White (arbiters of writing style) say:
Form the possessive singular of nouns by adding 's. Follow this rule whatever the final consonant. Thus write,
Charles's friend
Burns's poems
the witch's malice
Exceptions are the possessives of ancient proper names ending in -es and -is, the possessive Jesus', and such forms as for conscience' sake, for righteousness' sake. But such forms as Moses' Laws, Isis' temple are commonly replaced by the laws of Moses the temple of Isis.
As for possessive forms - that's even easier. In most cases, if something belongs to someone, use an apostrophe. If it doesn't, then don't. Okay, it can get confusing, but in most cases, it's not.