Installing over stove microwave
Danger!
Working hot is problematic, especially if you are not a pro.
Rental
A rental is not the same as owning your home. For the same reason the electrician owner had to pay someone else instead of doing it himself, you shouldn't be doing any real electrical work here either.
Use As Designed &amp; Tested
Most current models of over-the-stove microwave ovens (I checked a Whirlpool and GE but have no reason to think others are different) are designed to plug in to a standard outlet. Unless specifically authorized by the manufacturer, replacing with a hardwired connection will likely void the warranty and could lead to other problems.
In addition, if you ever need to repair the oven (and I've actually done that successfully on a similar oven after a thermal overload due to user error (a.k.a., food cooked way too long and caught on fire...)), you would not have an easy way to shut off all power while you work, because you couldn't simply pull the plug.
Proper Installation
No matter who is doing the work, all splices (with certain exceptions) must be inside equipment or junction boxes, not in ordinary cabinets.