Am I responsible for both my portion and my roommate portion of the rent?

Generally leases are joint and several liability. This means that, yes, you would be responsible for the entire portion.

How can I get out of jail on a probation violation warrant when you had no idea you were on probation?

We won't know either. An attorney would have to review the case.

Will I be arrested for failure to appear?

Hire an attorney to assist you with he matter. And are the people advising you attorneys?

File for a modification for the situation.

The place i am staying is being sold

A property sold is burdened with the lease associated prior to sale; with the exception of foreclosure situations.

Do I have to pay rent for a month I will not be there after giving my 30 day notice?

Your lease governs, however generally the 30 days notice means you pay for the 30 days after you give notice, whether occupying the space or not.

My girlfriends public defender failed to show for the court appointment on her arraignment.

You keep saying "we." Your girlfriend is the client in this situation, so the public defender may refuse to speak with you. But your girlfriend...

Is it legal to offer someone in jail a plea deal without them seeing a lawyer (and before their scheduled court date)?

She doesn't automatically get an attorney. She had to hire a private attorney or apply to qualify for a public defender. If she has neither, then...

Hire a lawyer to get it reduced to 14 over.

What constitutes a settlement agreement in Georgia?

Verbal means nothing in terms of a settlement agreement.