Does a travel eSIM come with a phone number?

Generally no. Most travel eSIM plans are data only, so they carry no local number for receiving calls or SMS. What you get is an internet connection, which covers app calling, maps, bookings and every form of contact that runs over the internet. Where a plan does include a number, its own page will say so explicitly.

Use an internet calling app as usual, voice or video, from the same account tied to your Thai number; the person at the other end sees you exactly as before. The only condition is that they use the same app. If you must dial a landline with no app, use a paid internet-calling service, which is a separate service from that provider and independent of your data plan.

No, and often you should not. A phone that supports two lines at once can keep the Thai line for calls and SMS while the eSIM carries data. What you should do is switch off data roaming on the Thai line so nothing is charged unintentionally. What receiving calls and SMS abroad costs is set by that number's operator, so check before you travel.

Yes. Those apps bind your account to the number at registration and then run entirely over the internet, so you message and call over the eSIM with the same account and the same history. The exception is re-registering or moving to a new handset, which usually needs a code sent to the original number — do that before you travel.

Enter your own Thai number in international format: +66 with the leading zero removed. Never invent a number, particularly on official or travel-related forms. Then pay close attention to the email field, because email is the channel through which you will actually receive news during the trip, whether the Thai line is on or off.