To go through these in order:
Yeah, basically. If you want to get fancy and have gambit slots to spare, one idea is to have a "heal if low on hp" gambit at the top of your white mage equivalent, and a "heal if not at full hp, when nothing else is going on" gambit at the bottom. It's up to you to figure out what works for you though.
After healing, one super basic, early game set up to consider is to have two attack gambits: Top priority is who the party leader is attacking, second priority is...whatever you want them to focus on. The nearest enemy, for example. Just having the former can be limiting if (for whatever reason) the leader hasn't attacked the enemy yet, so both can help out in that regard. Also, feel free to swap out "attack" for a spell if an enemy is weak to it. Other gambits to look out for are the "weak to element" gambits, and generally gambits that allow you to distinguish between different enemy types.
You can probably get away with a single setup for the general stuff, but you can change gambits at any time. So be flexible!
There are a few solutions to MP troubles. Using your full party obviously helps, and don't ignore save crystals even with the auto save, since they heal your party. There's also some licenses that decrease MP costs/increase MP regeneration. Finally, whilst I'm not super far in the zodiac version to be the best judge of this, you *do* have ethers at your disposal, so feel free to use them if needed.
You can definitely get by with just a party of three, but there's a lot to be said for the flexibility of a full party, especially with the job system. At the very least, if your main party dies, you'll have to switch in the reserves, so it helps if they can take a hit before using a Phoenix down or whatever.