Installing central air question about conduit from disconnect to panel

Hi, I have been lurking here for a while and enjoy the many informative posts.

Anyhow, I am installing my own central air system. I got an HVAC guy that is going to braze my lines and check my freon and stuff for a $100.

I have done lots of wiring before but I am unsure of something.

So I setup my outdoor wiring and my safety disconnect. I used those a/c whips (flexible conduit). Now after the disconnect where it comes into the house, it is long enough to connect the conduit directly to the panel. I did buy some romex and a junction box thinking it would not end up being that close. Is it allowed to run the conduit from outside (from the disconnect) directly to the panel? I could not find the answer anywhere. I have a copy of the NEC but its so hard to find answers in there sometimes.

Also my thermostat wire is 20 gauge and the thermostat wire in the condenser is 18 gauge, is it okay to connect those 2 together with differing gauges? I did not notice until after I ran the thermo wire through the conduit and all the way to the furnace.