-- Have you ever received an eviction notice?

I would not jump to notices, breach of lease etc just start with a conversation and tell them they are no allowed to be in your place. 

You will likely need to provide a paper trail proving you provided written warnings / cease and desist notices to the tenants for said minor violations.Even then, you never know for sure if the judge will rule in your favor.That is why it is always easiest to evict for Non Payment of Rent.

As long as proper notice was served there should be no issue. 

I'm in NE Ohio and while I don't plan to completely "self-manage" (ie, do maintenance/cleaning/etc. myself) I do want these properties to be close enough that I can A) check them out personally when needed and potentially tinker/add improvements on occasion myself AND B) if they are vacant for a weekend, go and enjoy some R&R on short notice. 

Deliver it and also post notice that you will be doing an inspection at a set date and time and then follow through.

We have already sent out a late notice.

We have definitely noticed that on the customer service side. 

Noticed my loan lender closing cost details shows they charged 10Months Property tax prepaid.

I don't let it go past the middle of the month without serving notice to vacate.