@Chris Hanisco - many times an owner who is selling has all tenants on a month-to-month lease. Ask your agent to find out. Read the lease and the detail on pets. Make sure the rent and/or security deposit collected are appropriate for the clean-up you may need to have done inside that unit.
I like this deal and would do it if I were you (given all you have shared about your situation). Read the āManaging Rental Properties Bookā by Heather and Brandon Turner.
I donāt know the Tenant obviously, but he/she sounds sketch. No one needs a week to spruce up a small home for a showing, especially not being the owner. Also, consider the Seller may want you to just pass on seeing that unit if he/she suspects issues lie inside and, given the fact that it is a hot market, the Seller mat feel the pressure is on you. Donāt allow that to weigh on your emotions. It should be in the lease that tenants can only push a showing off so far before getting charged by the Landlord. My leases with my Tenants do...
In Illinois, either party can get out of a Contract for ANY reason, except for price, within 5 days of signing. Check with your attorney on the rights of recision in NH. If favorable, I would make the offer and get a contract prior to seeing that side, given the HOT market. Have an inspector lined up and ensure the owner is getting you in that unit as soon as the contract is signed. Once the property is under contract that will slow other showings to other potential Buyers and give you time to figure out whether or not this is the right deal for you. Once the inspector shares her/his report with you (no later than 48 hours after they inspect) you should renegotiate the price down for all repairs needed to get that other unit rent-ready.
Be sure to follow the current lease for that Tenant and get him/her out as soon as the lease will allow so you can fix it up with the money from your lower negotiated price and then move-on with another Tenant. From your personal experience, you know it will not take long to find another Tenant.
Renters will be easy to find for many years to come. Just screen them right so you can minimize foreclosing over the long haul.
Read as much as you can on the real estate topics you are experiencing now, and hang in there with BP, they have all the right tools and info. And, I say that having absolutely no affiliation with them other than being a Member. PM me if you want to chat. We can get on the phone live, and it may be easier than email.
Good Luck! Bob