There are a lot of holes here.You typically can not evict for late rent if the PM accepts the appropriate rent and late fees.A PM should not give 1.5 months notice to move out AND file eviction...it should be one or the other.It's common for leases to automatically renew month to month after the initial lease period. 

HELOC's are a great way to go if you need a good chunk of money for a short period of time. 

Make sure you have a forwarding address for the tenant so you can mail your determination and refund (if appropriate) within the allotted time period.

If I acquire a second house subsequently, rehab it, rent it out (past the "seasoning" period), and try to refi it to get some money out to repeat the process, will I run into issues with the mortgage on my first home when the lenders see that I do not have income from a job to pay for the first mortgage, thus will refuse refinance of the 2nd house?

If you do build up equity over a short period of time, I would rate and term refinance into a conventional loan, and then move and use the VA loan again.

A few points: Per the Fannie may guidelines for the “delayed financing exception”, you can borrow up to 75% LTV, OR your initial purchase price (this can include closing costs), whichever is LOWERLots of people have had success with including rehab costs on their HUD / closing statements, so that the second part of the above guideline isn't the limiting factor, enabling a BRRRR-type strategy without having to wait the full 6 month seasoning period.

All auctions aren't cut the same so it depends on what type of auction you are talking about.Most online auction (Such as Hubzu) allow enough time for financing. just be sure that you will be able to have full access to the property during the DD period

A real estate wholesale generally occurs when a wholesaler enters into a contract with a property seller, who more often than not is looking to sell a property in a short period of time.

The seasoning period doesn't have to do with how you purchased the property.

Average inspection period?