As a landlord, am I able to give my tenants notice that I will not be renewing the lease agreement?

Increase the rent anyhow at lease renewal. 

Lease agreements or renewals with tenants, including any addendae.

I would be sure to give the tenants ample notice of at least 60 days that you won't be renewing their leases. 

They will usually take a large portion of the first month's rent (that can be negotiated) and rarely have a fee for renewals (unlike most managers).It might take a little work to find a good real estate agent that handles rentals that will give you a good price for just 1 unit.

Prorate her rent for the 5 days with proof that she stayed at a hotel (not the price of the hotel, but she needs to show she was staying at a hotel) and when her lease is up for renewal-give her notice that it is not being renewed (based on the fact that you said she's been late multiple times).

I recently bought a house in plano.I had a done inspection and found that the Upstairs AC was not cooling.I reported this to my realtor and asked sellers to repair it.Sellers never repaired the issue completely (they ...

You'll have to reference your state laws, but most of the time you can just refuse to renew the lease. 

Under federal regulations, institutions may obtain an evaluation of real property collateral in lieu of an appraisal for certain transaction types:Commercial real estate-related financial transactions in which the transaction value (generally the loan amount) is $500,000 or less.Certain renewals, refinances or other transactions involving existing extensions of credit, provided there has been no material change in the market conditions affecting the real property’s adequacy as collateral and there is no advancement of new money other than funds necessary to cover closing costs.Real estate-secured business loans of $1 million or less in which rental income from the property or income from the sale of the property is not the primary source of repayment for the loan.

In terms of not renewing their lease, they don't plan staying longer anyway as they want to buy a house in a year.