Will I simply be able to just sign my name, trustee, Mark S's revocable living trust and deposit to my personal account? 

3 months behind and still wants to stay another 3 months, disregards the eviction notice, and asking for their deposit back...

As long as your credit is good (I think around 650), you can borrow money from P2P sites.4. secured Personal line of credit - if your credit is NOT so good, and you have some assets like Certificates of Deposit or stocks, talk to your banker about opening a SECURED personal line of credit.

It can just be a one pager stating the important facts "purchase price, deposit, close date, conditions, parties etc.." then where you get serious have a lawyer draft out an agreement.. 

We had multiple offers on this property and accepted a full-price offer with a high earnest money deposit.

To your main point, no you won't get any money from them for attorneys fees or damages, beyond their deposit. 

Anyways she tried to say well cant you just take that from my security deposit and I told her no that in her lease it states that she will not get her security deposit back and that she needs to pay a termination fee.

For example, if the security deposit wasn't handled perfectly, the eviction may get dismissed, and you could end up owing the tenant money.- Even in the best case, the process is not fast. 

do they just deposit the full purchase and rehab costs into your account?

Certainly you can make an offer, but the agent will likely require a large deposit and pre-approval letter for financing or POF in your name (your bank account).