Can a USA citizen apply for green card for her sister ?

Yes it is permitted, but takes 10-20 years.

Can I apply for a travel document and use it to travel without the need to the passport? Thank you :)

Your best option is to renew your passport before you travel.

How can i still protect my temporary protected status and stay under f1 status

You are able to keep both provided you maintain the requirements of each.

Just wanted to know if i can no longer renew my Mexican Passport? any risk?

You may renew your Mexican passport.

What options exist to help my aunt spend more time here with me on a legal status?

You are not permitted to petition for your aunt. For immigration purposes, adoptions must occur prior to 16th birthday.

Is it against the law to enroll him in high school meanwhile he is with me ?

Yes he wiould as he must have F1 status and is not permitted to attend public schools.

Adjustment of status and NVC

While you are permitted to adjust status in the US, you do have to wait until your priority date is available for filing.

No repayment obligations for ACA credits.

Apply for legal status on humanitarian grounds.

There are no immigration paths due to an illness.

How can they help me ?

It totally depends on who the someone is, for starters. Repost.