You really need to contact a probate attorney to help you in this matter. He and she can outline your rights and responsibilities as executor. Many legal things need to be done to complete the process and there is a time limit. So sorry for your loss.
No. They go to the actual accounting for the property to calculate capital gains. The "$10 and other good and valuable consideration" is just legalese to satisfy the consideration requirement of the conveyance. If this is your home and you have lived in it for over 2 years, you may be exempt from paying federal captial gains tax if the capital gains is $250,000 or less.
You do with the proper written notice and subsequent failure of landlord to remediate. Here is a link that might be helpful. http://www.michiganlegalaid.org/library_client/resource.2005-05-30.1117489737707 Be sure you send the notice by both certified and regular mail so that you can testify as to mailing and the fact that the notice sent by regular mail wasn't returned.
You will need a deed to make a transfer. The transfer may trigger the accelleration (due-on-sale) clause in the deed of trust, but in my many, many years of practice, I have never seen a lender accellerate a performing loan. However, it is a risk you must be willing to take. Best of luck.
You have remedies. You must give proper notice in writing (I send both certified mail and regular mail - plus hand deliver, if possible) and opportunity to cure. Instructions and remedies can be found at www.texastenant.org. Best of luck.
Upon inheritance, as a devisee, you are entitled to continue to make the payments under the Garn-St. Germain Act without fear of the lender accellerating the loan. If you don't make payments, the lender can foreclose. The house will be yours, subject to the loan, and you can sell it, lease it, or live in it.