Real Estate in Trust? (Veteran: house, deed, taxes)

[dennis bran]

I am trying to determine whether my parents home is going into a "TRUST", upon death, or going into probate. The home is currently deeded to my father and mother (she has since passed away- deed not changed) . My father has set up a "Trust", to receve his assets when he passes, however, I do not know about the home. If the deed shows the home in his and my mothers name currently, does that mean that it will go into probate upon his death and then into Trust? I beleive the will was set up this way, but, I am not sure that the home will avoid probate and go into the trust upon his death. The ideal situation is to avoid probate, which can be timely and costly, so the home can be sold without having to wait for probate. His Federal ($250,000)tax exclusion is only good while he is alive or until the next year after death.
I need to know if the deed must be changed to reflect that the home is currently owned by the Trust versus him personally. And, if this is the case, does he lose his Veterans discount for the Real Estate Taxes and does he lose the exclusion for himself if the house is sold? Can the home be put into a Trust now, and keep those benefits if it is?
Is there and agency in NY that I can talk to that may confirm whether or not a Trust even exists?