1) Not really a question, but even having another character on watch doesn't seem like it would have helped too much. Being asleep (i.e. unconscious) is nasty bad.
Yes, but these are adventurers. They should wake up easily because they often are in constant danger.
2) What's a reasonable DC for waking up sleepers by yelling? My gut says its "hard", so DC 20. A couple players felt that was too high. Since everyone rolled under 15 or over 20, it wasn't an issue. Feedback welcome, though.
10 if in a dangerous area, 15 if the PCs feel safe. In real life, a lot of people sleep more lightly in unfamiliar settings. Some don't. But since this is a game, that's how I would view it.
3) Can Alarm be used to effectively protect a camp? It says 20' cube, which isn't much more warning than the rogue had when he yelled. It would have made the "yelling" automatic, but a larger area still seems better. Can the 20' cube be reshaped, say, to a 5' think ring/square that's hollow in the middle. That seems against both RAW and intent, IMO.
An enterprising party can make any approach to the camp go either through the alarm area, or cover other areas like ones with bells on wires. But by RAW, the shape of the spell cannot be changed.
4) Does wearing armor negate a long rest (i.e. sleep)? Could the tanks still wear light armor and sleep?
The tanks can wear any armor and sleep. They can even sleep with a shield strapped to their arm (some DMs might not allow this, but RAW doesn't say anything about it). This can occur in real life too. This is a game. No need to add house rules for things like this.
5) How deep is elven trance? I read it as still being effectively asleep. The advantages are that the elf only needs 4 hours and doesn't need to remove armor or lie down.
It's effectively asleep.
6) Do familiars need any down time? I ruled that they needed some recharge, so they disappeared for a few hours, but were around for their masters' watch.
Up to you as DM.
7) Any other thoughts on avoiding a dirt nap when taking a long nap in 5E?
Well for one thing, wolves howl when they get close to prey. They also do not always attack immediately. They hang out in the dark and threaten and build up their courage. Technically speaking, the upright bearing of people is different than most wolf prey and is reminiscent of bears that stand upright. Wolves tend to try for weaker prey. Wolves also do hit and run tactics on prey to find out if the target is prey or predator. Wolves often scatter if some of them are killed or if the prey looks too deadly. And finally, wolves tend to avoid humans as prey. Instead, they prefer to follow humans and scavenge after them. Historically, wolves have evolved to mostly avoid humans.
So if you send in 6 wolves and have them fight to the death, that's ok, but it's very non-wolf-like. Not that this matters in a game.
As far as more intelligent predators, that should be handled by PC planning. Intelligent predators can do just about anything. But both intelligent and low intelligent predators should often cut their losses at some point. Sometimes, intelligent predators are under orders, or defending their homes, or some such and should fight to the death.