New landlord don't know what to expect

[Adam Hinkley]

Hi all,

New to BP and new to be being a landlord as I close on my first property on Friday. It's a duplex that will be owner occupied. I have a few questions about how I should proceed in the first few months of owning the property and will really appreciate any help I can get. 

Few details first, the other unit is rented by a single woman who has lived there for 4 years and is on a month to month lease with previous ower. She currently pays $895 and is paying under market value as previous owner never raised rent, similar 2br/1ba properties rent for $1100-1300 a month. Ideally I would like to keep her as a tenant and she would like to stay according to previous owner has been a good tenant. 

My plan is raise her rent slightly to around $1050 to get closer to market rates, plus I plan on doing some upgrades (deck etc..). This would help me minimize initial costs until I get settled in to the place. Also I was planning raising rent July 1 and having her sign a new one year lease then

Interested in general as to what people thing of this plan  

Couple questions  

Once I close what happens to her old lease? Is it null?

Do I need to have her sign a new lease right away?

My lender included a security deposit and rent proration credit on my closing cost, does this mean I can't collect security deposit from the seller or current tenant?

Sorry for the long post, and thank you for anyone that has some advice!!