Pronouns,Am I Chosing the Proper One????

I have a few sentences here. I need to make the pronouns proper if they are not. I will select what I think is correct. and If I'm wrong, please correct me. Thank You.

It is difficult to go to the store on a bicycle.

I believe this sentence is correct.

My shirt is cotton but her's is silk.

My shirt is cotton but Beth's shirt is silk.

It doesn't matter how rich people are, you can always find something fun to do in the city.

I'm completely confused by this sentence. Please help unfreeze my brain.

How about? No matter how rich you are, you can always find something fun to do in the city.

A student who fails has no one to blame but hisself.

That is a sexist pronoun, correct. I believe the correct version would be:

A student who fails has no one blame but themself.

Every parent wants his or her child to their best.

Could we say? Every parent wants their child to their best.

All of a sudden, your dog bites a neighbor and you get sued.

Say what?! lol Umm. Help. ??

The committee has not yet finished thier report.

I believe this sentence is correct in its current form.

Either Bob or Ralph forgot their bag in the work room.

Both Bob and Ralph forgot their bags in the work room.

Neither Bob nor Ralph were able to do his homework.

Neither Bob or Ralph were able to do their homework.

I would appreciate Ted helping Bob and I with the work.

We would appreciate Ted helping Bob and I with the work.

Bob and I would appreciate Ted helping us with the work.

When a student forgets to do his homework, they will usually not get a second chance.

When a student forgets to the his/her homework, they will usually not get a second chance.