Sasha,

a new inspector in my township came to check my new kitchen and
upstairs plumbing. He rejected my work due to several problems

I guess I'm lucky. We built our own house last year (Washington State),
and did all the foundation, framing, plumbing, electrical, etc. ourselves.
We had at least 7-8 different inspectors over a 2 year period, and every
single one of them was pleasant to deal with, helpful when I had questions,
and usually commented on the excellent quality of our work. We'd call in an
inspection and they always showed up the next morning. We passed every
inspection without a single correction needed.

Our electrical inspector was a little apprehensive when he first showed up
and realized we did the wiring ourselves. But once he saw our work met or
exceeded all codes, he seemed very impressed and was more than happy to
approve our work.

The closest thing to a "hurdle" was the health department. They didn't
visit the site, but wanted me to draw up the plot plan in their office.
They seemed concerned about the proximity of our well and septic
system. Obviously my drawing was NOT to scale, we have more than the
minimum distances, and the system had been inspected and approved twice
already in the past several years. It only took a few minutes to straighten
out and wasn't a big deal, but that was the closest thing to a problem we
encountered.

1. He said my house must have 1 3" vent and two 2" vents. I thought
that vent size is determined by number of fixture units it vents.

Unless codes have changed, vent sizes ARE determined by fixture units, but
at least one 3" vent is required to reduce the change of frost/snow
closure.

In our house, I wanted to minimize the number of roof penetrations, so we
just have the single 3" roof vent (to match our 3" main drain). I ran 2"
vents from all fixtures in the house and tied them into the single roof
vent (with a 3" trunk line running through the attic). The inspector
approved it easily and said it was way more than I needed, but it
accomplished the single roof vent I wanted.

2. He insisted toilet must have a wet vent instead of dry went that I
put. Why does toilet must have wet vent and why dry vent is no good?

Hmm, never heard that one before. Usually the concern is that the toilet is
placed too far from a vent, which could lead to siphon and drainage
problems. If I remember correctly, the toilet drain can run a maximum of 6'
before it is vented (2" minimum vents for toilets). My 3" toilet drains run
about 2 feet before a 2" vent heads off to the attic.

3. He insisted that rubber Fernco couplings that I used to connect new
PVC DWV with old copper plumbing are prohibited

I don't know your situation, but I'm not sure if they are allowed in
"concealed" locations? I could be wrong though, as they are the standard
way of connecting no-hub cast iron piping.

I used one in our attic to connect our 3" PVC plumbing with a 3" ABS
section to stick out the roof (didn't want a white pipe above the roof, and
didn't have the vertical room for male/female adapters). I also used a
couple in our crawlspace for our bathtubs and master shower, as it made
installation and future maintenance easier.

Good luck!

Anthony