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.
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.
It would be impossible to be charged for trespassing because both siblings are owners. On burglary, there must be a breaking into a building with intent to commit a crime, and you can't break into your own property. If there is any doubt, contact local law enforcement and run this by them. I would suggest you both establish boundaries so that everyone can live in peace. For what it is worth, occupying sibling should "lease" the other's portion and pay rent while in occupancy for the...