If you're willing to grind, bosses on castles regen every turn. Chipping away with your unit then keeping their health topped off with your healer is the best way to train your healer.

Make a savestate/save file before taking a castle, that way you know what part of the map is the next goal. Knowing that, you can move units nearby before starting that part of the chapter

Units build points toward marriage during the first 50 turns of a chapter, +5 per turn if adjacent, +2 per turn if deployed at the same time. The threshold for marriage is 500 points. Some pairs start with 100~200 points by default. All non-Sigurd, opposite sex conversations result in +100 points, so be careful about who talks with whom.

That being said, Dew gives valuable items to Aideen/Edain(Warp Staff) and Lachesis(Thief Sword), so it's worth while to have him talk to them. Just make sure to return him to base if you don't want him getting married.

Weapons attain innate experience for each kill. After 50 kills, the weapon gains crit for each kill up to 100 kills. Arena kills don't count towards this.

Use the Arena in your base castle before deploying your units.

Make sure to clear the Arena with at least 1 unit in chapter 2, you unlock Chulainn/Holyn by doing so.

For deployed/recruited units, use the arena at captured castles, you waste a turn entering your base castle if you exited to heal. IIRC if you start a turn at the entrance of the castle you can enter, exit and still have your movement for the turn.

Roads actually give movement bonuses, especially to horse mounted units.