It is irresponsible to answer these questions without a complete review of the estate, the will, the assets, etc. The other attorneys are absolutely correct. If you do not have a probate attorney, you should consult with one immediately. You have a fiduciary duty to the beneficiaries/heirs of the estate.
You can go to the recorder's website and check title on the property. If the aunt held the property in joint tenancy with her dad, then she could have transferred title to her following his death by submitting an Affidavit of Death of Joint Tenant. Otherwise, she could not have transferred title. If your husband's mom is the named executor, she should meet with an attorney familiar with probate.
I agree with my colleagues as to your options. I just want to add that probate occurs in the county where the deceased resided. Since Arizona law applies, you should meet or speak with an Arizona probate attorney to determine the best course. A letter from that attorney to the girlfriend might be the way to go.
The children are the beneficiaries. If they are minors, a guardian of their estate will need to be appointed to receive any assets for their benefit, or monies will need to go into a blocked account for their access upon becoming 18 years.
The administrator is not responsible personally for any expenses. The administrator is responsible for gathering and marshaling the assets and monies of an estate so that the estate can pay expenses. If the administrator fronts monies for some reason, and it was money necessarily spent on behalf of the estate, the administrator may be reimbursed.
Sounds like you have an attorney. If you don't have faith in your attorney, and more important, if your attorney does not practice regularly in guardianship court, you need a new attorney. Hiring a private investigator might be an option. Other discovery can be done. The parental preference is strong in guardianship court. If you are fit, it is difficult for you NOT to be able to terminate a guardianship.
Depends. Has he added you to the deed? Has he prepared a will giving you the house in the event of his death? If no, then your interest in the house at the time of his death would be 1/2 of whatever community interest you might have gained during the marriage. If the house was paid for when you married, you'd have none. If mortgage payments have been made with income from the marriage, you would have an arguable interest in any equity since the marriage. Based on the market, that could be...