When a rental is taken out of service for personal use the accumulated depreciation goes away over a short period of time. 

Were they all completed within the same 12-month period, or did it take longer?

It’s a full-time commitment, especially when you’re just starting out.

This way you do not necessarily need to identify a new property within the time limit.

I assume you would use your own $ to put property under agreement and get investor to close around same time, but if not you will have 1-2 months of holding costs plus time to renovate and time to sell the property.

When you do a little extra work ahead of time, the process goes so much more smoothly.

It is not uncommon for auctions like this one to get rescheduled multiple times before ever actually making it to the courthouse steps. 

Assuming your property is in Utah (like your profile indicates), here's the state law from a basic internet search:In Utah, a tenant who abandons a rental property without notice is liable for the lesser of the following: The rent remaining on the leaseThe rent plus the difference between the fair rental value and the agreed-upon rentThe cost to restore the property to its original conditionThe landlord can also remove the tenant's belongings and sell them if the tenant doesn't claim them within a reasonable time.

We are planning to live in one unit and rent the other half out of a duplex, then rinse and repeat this process as many times as possible over the next 5-10 years.

Give them notice that their lease will end and you expect them out by a specific date/time.