The answer to all of your questions would seem to be YES. They can do all of that.
I am guessing that you got 10 days behind in your rent and THEN you got the 3-day notice to pay rent or quit. Did you pay the missing rent before the 3 days notice was up?
You won't get a 30-day notice. If you didn't pay the missing rent before the 3 days was up, you were supposed to have left after the 3 days. If the landlord filed an eviction suit, it will be very difficult for you to get him to change his mind. After the 3 days were up, he was no longer required to cooperate with you in accepting rent, and being a month-to-month tenant has nothing to do with it.
I suggest that you go and talk with your landlord, say you are sorry, offer to pay all of the back rent plus his expenses in filing the eviction suit, and even ask if there is anything that you can do for him to change his mind. He may have another motive in taking the position that he did: for example, if your area is under rent control, it may be that he can raise the rent to the market value if you leave, but if you stay he cannot (vacancy decontrol). If that is the case, you should offer to move out and move in again, and accept the higher rent.
