Hi, I don't know that much about home repair in general. I am having
some work done, and I want to know if it is done correctly or not.

I am having a heating vent installed in a new finished office. He is
using metal duct, but he is only taping it closed and together. It is
heat tape with red print on it but he is not using any screws. I
question him about this because all of my other duct work uses screws,
but he tells me that using tape is better better because it prevents
all leaks? My question is, if this is really the right way to do it?

And my oven hood vent, we originally agreed to create a new vent for
it through my vaulted ceiling, then he said we could go through the
wall, and then through my unheated attic. I was fine with that, but
upon further investigation, I found out he connected it to my bathroom
4" bathroom duct. I talked to him, and he will change it to have
it's own duct. He also used an insulated flexible duct, when I did
research, I found it stated that you should use hard metal duct. He
said it was better to use flexible insulated duct so you don't get
return cold air? Is this right, or should I ask for rigid metal
duct?

Can you just glue and screw plywood to a cement basement or do you
need a moisure barrier between the plywood and cement? He is doing
this to raise the level of my office to the same level as the tile in
my hallway so I can float engineer hardwood on it.

Just want to make sure I am getting my home improvement done
correctly. Thanks,

Lulu