Tri-Plex in Kansas City, KS. Inherited tenant questions

[Luis Silva]

Hi all, 

Thank you in advance for reading my post. I am currently in escrow on a triplex in Kansas City, KS. The leases/tenant structure is as follows:

Unit 1: Studio - Rented for $440 - One year lease (Ends May 2018 - just resigned)

Unit 2: Studio - Rented $480 - two year lease (ends May 2019 - Just resigned)

Unit 3: 2 bed 1 bath - Rented $625 - Month to month lease. 

1) On Unit 1: the lease states that the tenant pays 2 installments for rent (she pays on the 1st and then again on the 15th). She also pays in cash. Do I have the right as the new landlord to renegotiate these terms? What is the best way to go about doing this? Mainly, I just can't accept cash... I probably could work with the two installments but that is a bit of a pain for me.

2) I am worried about inheriting tenants. The landlord says that unit 1 has been rented by the same gal for several years and unit 2 (just resigned for 2 years), is a great tenant that pays on time every single month. What can I do to validate this information and/or make sure they are good tenants?

If you can't tell, I am new to property management so any feedback is welcome and appreciated. 

Thanks a bunch!