I understand the lawsuit must stop if the tenant pays everything that's listed on the unlawful detainer summons, but what if a new month begins before the court date?

I would contact the police if any unlawful activity is suspected.

Then I went on county website and looked up owner's unlawful detainers (?)

It is also borderline unlawful and can get you in hotwater legally. 

Bought a Foreclosure in my single member LLC and I need to file an unlawful detainer eviction. 

If you do allow it, I would get him to sign a waiver for it so he can't come back and claim you unlawfully kept his deposit.

The termination notice, called a Three-Day Notice to Pay Rent or Quit, gives the tenant three days to pay rent or move out.If you haven’t followed the rules, and the tenant doesn’t pay or move within the specified three days, you’ll have to file an eviction lawsuit (also called an unlawful detainer).

Many are giving wholesalers a bad name by doing shady deals and having unlawful practices.

All communication in writing so you can present it to a judge at an Unlawful Detainer hearing.3)After raising the rent, I am 100% sure that tenant will begin to argue and make claims of the legality of raising the large amount at one time.How would you respond to baseless claims of the legality of the rent increase?

Someone may claim (unlawfully) the homeowner tax exemption and still rent the property.