Can someone on a J-1 Visa, opt to change their visa and stay with family in the US for a period of time?

An F status might be an option, but the problem with any non-immigrant status is that the person promises to return back home upon its expiration.

Can my husband travel on advance parole with expired F1 visa?

If your husband filed for adjustment of status based on marriage to a USC, he should be able to use the advance parole to travel safely.

Have I accumulated an illegal presence? And can I apply for green card through employer?

Most likely, you did not accumulate the unlawful presnse, but you will need to leave the US to get a visa if you are sponsored by the employer.

If Fiance visa is being processed , can I come and go back into the US if I live in Canada and have employment in Canada?

You should be able to use your Canadian status to come to the US as a visitor unless you will require a visa, and the consulate will decide...

How to prolong B1-B2 (tourist visa). What are the options?

You may extend your status for 6 months once.

Can getting food stamps affect my husbands immigration status?

If you are a US citizen, you will need to find a joint sponsor to petition your spouse.

You should wait for the RFE. USCIS will mail you a request for that form.

Will I be eligible to get a 10 year green card?

You will be eligible for a 10-year card if your wife files for you now.

If the basis for EAD was pending i 485 and now, I 485 is no longer pending, you will not be able to receive the EAD, I believe.

Travelling with a refugee travel document

You should not have problems coming back to the US. As for the visa requirments to other countries, you need to check with consulates of those...