It depends which line you switch it on for. On a travel eSIM whose plan you have already paid for, usage comes out of that plan and no new charge appears. On your home line, the rate is whatever your domestic operator sets, which we do not know and should not guess at. Ask that operator before you travel.

Generally yes, because text messages do not travel over the data channel. As long as the home line remains switched on and can attach to a local network, messages continue to arrive; what you disabled was data only. Charges for sending or receiving texts abroad still follow your home operator's rates, so it is worth asking them too.

Attaching to a network and being allowed to move data are two different stages. Once the phone has attached, the network name and the signal bars appear, but data flows only when that line's roaming switch is on and that line is the designated data line. Check both, then cycle aeroplane mode and restart.

Enable it at home, and it is better to do so. The setting does not require a signal from the destination network, and doing it calmly gives you a chance to confirm you enabled the right line. On arrival the phone will attach to a local network by itself once you leave aeroplane mode.

Not always. The regional name is just a label; the real coverage is the list of countries printed on the plan page. Go through your itinerary country by country before buying, because that list differs between plans and between providers.

At home your domestic line is not roaming, so the switch has no day-to-day effect. Turning it back off is still a good habit, because the next trip may come up at short notice and you will not remember leaving it on. An expired travel line can simply be switched off altogether.