My regrets on your father. For the mixed use, assuming no major defects, I would do a cosmetic upgrade for the store, paint it white and maybe put in floor tiles. Commercial tenants usually do their own improvements. Are there good commercial brokers in the area? You might want to look up what is for rent on loopnet to get an idea of comps.
For the three family that is not fully occupied, I would handle one floor at a time and fix up the vacant ones. The other property seems stable.
Since you work a lot, I would get lock boxes for each property so contractors can get in easily. I would hang out the carrot to them by saying I have 9 units and I am looking for good people so if you do a good job here, more work down the road. Then, start getting referrals and use yelp for service providers. Also, get as much automated as possible, like paying bills, Meter readings, etc.
Good luck, I took over my family's property 5 years ago(my dad is still alive) and it was nuts at first. I was running back and forth trying to figure out everything. Then I realized I was wasting everyone's time and concentrated on getting good help. But, you have to learn so just realize hopefully in a year, you will be in a better place.
