acquiring new tenant without lease

[Ty Hogan]

Hey BP community, 

I am closing on a Duplex to house hack at the end of the month and will be acquiring an existing tenant in one of the units. The tenant was renting from his mother and was paying $550 (market rent is about $750). This tenant also smokes inside the unit and has been for years. It is my understanding I must give him at least 30 day notice to vacate if I decide to get him out so I can rehab the place and chose my own tenant. If he is willing to pay the increase in rent I will probably keep him month to month until spring when I can rehab and get It ready for a better renting season. 
My questions are: 

1. What do you suggest about how to bump his rent? doing it all at once will likely push him out, but at the end of the day is that such a bad thing? 

2. What happens if he gets mad and destroys the place, since there is no lease in place am I now responsible for the damages? 

3. what if he does not want to sign the 30 day notice to vacate? 

Any advice on how to deal with this sub-optimal tenant without a lease is appreciated!