If it's a month to month, you may be able to give them a 30-day notice immediate after purchase. 

I’ve noticed that properties are leaving the market 12-24 hour after listed.

They use noon as an expiration in case a new tenant begins tenancy the following day to have enough time to get the unit ready - which was the case for me.Then tenant provided me proper notice by text message a few days before the 60 day required notice back in May. 

Since I must give 28 days notice, I can have them out by September 29th.

If you're even or ahead, you've learned a valuable lesson. 

The reason was that if it ever leaks or there is an issue the tenant will tell me right away it is in everyday view so an issue will be notices imidietly (no celling to repair or paint).3.

I noticed that you can finance a purchase made through Alex Cooper but they require the loan application to be made within 7 days of sale, has anyone used financing to purchase a property through Alex Cooper or other online auction websites?

If you could take the 500K and the current equity and invest that at 10% cash on cash you would come out way ahead. 

This isn't a  question that can be answered ahead of time since all markets are different. 

I drove by the property and noticed that the issue has been taken care of.