Your units can always heal in your borders and in neutral land. They heal 1HP per turn, if they do not move. Armies can heal in any land and heal 1HP per unit in the army.
Units in a town with a barracks will heal fully, if they did not move.
Edit way late I see.
Did units not heal faster if in friendly towns? IIRC (I might be mistaken)
Units heal 1 hp: if they do not move on friendly or neutral territory.
Units heal all HP if they stay entire turn unmoved in town that has barracks.
Units heal 2 hp/turn per turn they stay unmoved in friendly town that has no barracks (I might be mistaken about this)
Battlefield medicine minor wonder allows units to restore 1 hp /turn when stay unmoved on enemy territory.
Key of restoring HP is not moving, this even means that 1/3rd movement point you waste to go to the city means unit won't recover that 1 or all hps. As Fortifying and/or sentry orders do not take turns, same rules apply to fortified units - guaranteed they did not move before fortifying.
You can skip unit moves with space bar and can see if unit has moved thanks to green bulb that is near unit.
I avoid building too much improvements on pangea but arch is different thing
Don't think "I should avoid building improvements at all costs", think "What long term benefit would city gain if I build improvement there and is it worth losing those 80 shields at the moment". If you need to drive AI off your isle, then building 2 swords and a spear could be much more valuable than building marketplace.
I feel that I should have every commerce unit available to me and can't resist the temptation to build all multiplier building available at the the home island, also using many sea tiles for commerce harvesting by building harbor is also too tempting. The improvement building starts after researching construction. If needed
Look at corruption, if town has more than 50% corruption, building anything is not worth in it - just convert these towns into science farms - try to produce as much excess food as possible and then remove as many citizens from working and make them into specialists.
If town has less than 50% corruption, building courthouse followed by whatever other improvement is usually worth it. Think it about - why would you waste your time and money onto town what could produce 5 breakers max, after 100 turns (until you build courthouse, harbor etc.). instead of wasting your time you could hire 3 specialists who build 9 uncorrupted breakers + min. 1 gold (by building wealth) per turn
shl7070
I will even slowly depopulate some towns to increae efficiency of the main cities (by building workers then disband at 1 pop). Overseas cities get nothing except that one city on each island have barracks (and harbor if there is connectable resource).
Your core is your center, it needs to be improved. There's nothing wrong about building workers from size 4 capital - it'll quickly get its pop back to size 4 and will improve itself and other core towns around it. On other islands - keeping one spear in every coastal town and maybe 1 or 2 offensive units per island is far more than you usually need even on monarch
I keep one 'static defensive unit' in every larger group of towns. Every border town (that Ai can reach) gets 1 spear and 1 spear and/or horseman is fortified "behind town" so they reach several (seven or more) border towns within turn or two - this guarantees that AI does not capture my towns.