Very good.
Road bikes can't have flat bars (mtb) or bars that end facing forward or upward (TT bars, aero bars, mtb bar ends).
Crits are usually up to 2 miles long per lap, typically 0.5-1.2 miles. They can be timed or they can say it's "x number of laps".
In a dead heat in a crit they can rerun the last lap. I haven't seen that happen in the one crit I saw that ended in a dead heat. At Worlds when Taylor Phinney got 3rd he and another rider shared the podium for third. The reality is that usually a dead heat is kept a dead heat.
Free lap is void typically 8 km or 5 mi to go.
Mechanical failure justify a free lap, so a flat tire, broken saddle, etc. Things that don't justify a free lap is if you drop your chain or if you get delayed by a crash.
You're not supposed to push or otherwise assist another rider except for a particular track event. However if you are doing a polite thing (you give your teammate a small shove to give him a prime etc) then it's usually okay. Giving your teammate a slingshot is not okay.
Yes on bar plugs, your bars much be plugged when you start a race.
Socks aren't required. Your shoulders need to be covered in mass start races (TT sleeveless is okay).
You're supposed to wear your team colors or plain (manufacturer logo only) if you're not on a team/club. From Cat 2 up you have to wear matching kits. In Cat 3s and down you'll sometimes see riders on the same team wearing different versions of their kit, like last year's shorts or whatever. Cat 2 and above that's not allowed. This is to make things fair so everyone can identify someone on a given team.
Remember that whatever the official says at the line goes, supercedes the regular rule. For example at one race the official said there was a free lap rule in effect, even though the course was technically too long to have a free lap. The official knew it was too long but decided to allow it based on other circumstances.