Be the Property Manager and the repair man: Basically you're the RENAISSANCE man and if this is your first home I would for do this for not only saving money but for the experience and skills to know who to hire in the future.4.)

My computer repairman was selling his home but it needed work and he didn't know what to do. 

If the tenant doesnt like waiting , too bad , we all have to wait for things , I have to wait for the cable guy , or the AC repairman where I live , so will the tenant if not , it doesnt get fixed

Most leases require anyone over the age of 18 to be on the lease. check your lease. if it does and you have proof photos etc of more then lease tenants living there (neighbors testimony helps too)I would do a surprise visit as receiving take along someone who can look and act like a hvac or furnace repairman.

Also if the tenant calls for a repair man with out letting the landlord know, then the tenant pays for that too.

I sent out a repairman who checked burners, oven and broiler and all work fine.

Also, don't put much stock in a repairman's assessment of whether something was done properly or not. 

This was before I was an agent, I was 23 and working as an HVAC repairman and was fixing a furnace for this woman who happened to be a real estate agent and we just got talking and the next thing I know I'm buying I'm a house.

They generally won't bother a hired repair man.

You you simply tell them when the repair man is coming as Christopher said.