Your strategy is spot on in my opinion.
I'm currently 6-months into house hacking my first property in Madisonville. So far so good. This area is flip central and changing rapidly. Very exciting. I went with the FHA 3.5% down strategy as others have mentioned as well.
I'd suggest practicing running the numbers now through this winter. The BiggerPockets calculator is extremely helpful. I personally viewed the Pro Membership as a small expense to avoid making a larger and more costly calculation error. I'm strategizing my next purchase for Spring 2021 as well.
My thoughts/answers to your questions:
1.) I bought right when the world was shutting down due to COVID and you might be in a similar situation with this next waive. My initial offer was on March 21st and I closed on May 15th. I would reach out to a lender 90+ days before your target closing date for a pre-approval. I'd also get onboard with a realtor 90+ days before to talk strategy. More time is better than rushing in my opinion. Don't make a bad purchase because you feel you need to buy before your lease ends. Be flexible and think ahead in case your search runs longer (i.e. AirBnB, month-to-month lease, etc.). I'm accounting for 15 days for a pre-approval, 30 days for searching, and 45 days for closing on my next purchase.
2. Haven't used any contractors or handymen yet since the property is a full reno.
3. Talk wants versus needs so you can at least cover the list of needs. Then have a plan for how long your partner would be willing to house hack. I got my wife onboard with a 3 month old baby by explaining the financial benefits, having a clear need list (i.e. 1,2,3 bed, side-by-side vs over/under duplex, garage, etc.), and having a target move out date.
Good luck! Let me know if you have any further questions.