1. Circling the arena, don't just trot up and back and waste the time - I put my horse in shoulder in, then to travers, then to shoulder in again, ask the strides to come bigger and smaller etc. While also letting the horse get a look at the arena. Trot down the longside on the left rein - depending on the rules of the club and level of the competition, you can either just trot directly in front of the judge to give them a look at your number, or walk up to them and tell them your name, horse's name and number.
You then trot back down the longside, on the other side of the arena. Depending on your horse (and this just takes regular shows to work out what is best for your horse) you can either halt before you get to the end of the arena, wait for the judge to ring the bell and go straight in. Or keep the horse moving around at A until you hear the bell.
2. You may only enter 2 consecutive levels in dressage, so 'preliminary and novice', 'novice and elementary' and so on. Obviously there's something wrong if you're entering a low level, and the riding in a higher level on the same day/weekend! If the show is offering 2 tests per level, then yes, you are more than welcome to ride two tests to a level. Generally you can only ride a maximum of 3 tests in a day.
3. Protocol really depends on where you are. If it's a rated show, then you'll want to 'behave' respectfully, if its just a local 'come and try' show, you have a bit more leeway.
Avoid bringing a dog - though many still do, against the rules, it drives you crazy when you've got a dog barking at your horse all day. I've been to competitions where dogs have gotten loose and run across the grounds, through horse's legs, right through the middle of a test.... needless to say, the owner took a long time to redeem herself.
In the warmup, trying to find yourself an area away from others. Ride left shoulder to left shoulder (could be different in US-check with the federation) in the warmup if you pass another horse. Faster gaits have priority on the track, so if you are walking, stick to the inside tracks to allow trot and cantering horses room to go past. Lateral work has priority over all paces.
Avoid cutting people off in the warmup, it makes them mad ;)