I am in the process of filing for my greencard but my cosponsor's paystubs are hand written! Will that be a problem?

Handwritten paystubs are not a problem if there is additional evidence of income. It is a good idea to get a joint sponsor with sufficient income.

If no objection waiver for J1 research scholar gets denied, can I still apply for J1 alien physician or not anymore?

If the no objection waiver is denied then you cannot proceed with the application.

K-1 visa embassy papers

Now is a really good time to have an attorney help. Proof of employment means proof that the petitioner has a job now and is getting paid now.

It is a good idea to have an approved advance parole document in the event there are issues, but as Puerto Rico is part of the US there should not...

Can my foreign spouse be under 18?

Yes a spouse can be under the age of 21. However, there could be issues in the US with the age as young as 15.

Yes it is completely possible that you will not get a decision in 15 days. To get a complete copy of what has been filed ask the lawyer, and also...

I came to the US on a B2 visa and was granted 6 months which will expires in June 2015. Can i take short courses in Electronics?

Yes you can take the courses without violating US immigration law.

Can i apply for a green card now?

Some person or company must petition for you first based either on a family relationship or prospective employment.

Spouse Sponsorship (Affidavit of Support)

No you cannot. Given your circumstances your wife will either have to show enough income on her own or you will need a joint sponsor.

What will happen for the people on a temporary green card if the supreme court rules against same-sex marriage this year ?

The federal agency would respond based on what the Supreme Court decides.