As others have said, this stuff varies widely from location to location, as laws are different, but here's my understanding...
- What rights/protection do I have as a tenant? My contract (which was valid until end of 2016) states that if the landlord wants me to sign a new contract with different terms, he has to send it 90 days in advance, then I would have 30 days to accept or decline. I think the notice period is 30 days according to the local rules in the same situation.
Your rights are basically that your current lease must be honored, but no more than that. If you're currently on a verbal month-to-month, with no contract, I'd expect to either be notified that you have to move out OR receive a new lease to consider/sign once the sale is done (but any prospective buyer probably won't be allowed to contact you until the transaction is complete, and will probably be following the advice of their own lawyer). Either way, sounds like you'll at a minimum have 30 days' notice if you are asked (or yourself choose) to vacate.
Tenants have a lot of rights... but only as long as there is a valid lease contract in place.
-Does it make sense to ask the current landlord to formally sign a new lease for 2017 (including the month to month clause) before he sells the house just in case?
You can certainly try it, but there's a pretty good chance your current landlord purposely let things go all casual-like in order to make it easier to sell. Many buyers would prefer to not be beholden to previous leases.
-If a new owner wants to raise the price too much and make it a 1 year lease instead of month to month, what is the best course of action? I can try to negotiate in this case but need some advice on how to do it.
... it's the owner's prerogative. They can set the rent however they want, and set the lease length however they want (though obviously, you don't have to accept it). If you don't like what you're offered but want to stay, you can try to make a case for your excellent payment and quietness and cleanliness history (and ask your previous landlord to vouch for you), but it's going to depend a lot on the new landlord's plans. They may immediately want new 1-year leases at market rates, or they may value the stability of existing tenants.
-I paid a deposit of about $2.5K when I moved in. What normally happens to the deposit when the owner changes? My understanding is that it gets transferred to the new owner.
It should be transferred to the new owner. They should give you some sort of receipt or semi-official notice after the sale closes.
-Any other tips from more experienced tenants and landlords would be highly appreciated.
If you have a good relationship with your current landlord, just ask about their plans! My husband and I bought a 2-unit building last year with existing tenants in one unit; the seller flat-out told us at the showing that the current renters wanted to stay, and the seller would actually give preference to a buyer who would honor and even renew their lease. (There was competition for the property; and in our neighborhood, it's becoming really common to de-convert 2-flats to single-family homes... so the fact that we wanted to maintain the building as a 2-flat and considered existing tenants a plus rather than a minus worked in our favor.)