I have the same basic questions, @kirillan10
Here's what I know so far. Hopefully this thread will reveal further details.
On a typical phone, the eSIM activation does seem to reveal the hardware identifiers to the carrier. I don't know if Graphine has the ability to block or anonymize these. However, I doubt that it currently does.
In order to activate an eSIM on GrpahineOS, you must install Google Play Services and GSF. Then, you must grant Google the right to manage your SIM cards. Now you can install or remove the eSIM, using Google's software. Once installed, you can technically remove Google Play/GSF, although that could possibly cause issues if you ever want to remove the eSIM later. But by then, Google has presumably exported all of the data it wanted, so...
The other option some people say works, is to install the eSIM using the stock OS, prior to flashing the phone with Graphine. I don't really see this helping much by way of privacy, though, since Google can export your permanent identifiers at that time, too.
I can't really provide specifics for question 1.
Questions 2 & 3 I have no clue about. You can "disable" your other SIM, or if it is physical, you can pull it out. That way it is not present or active while Google is provisioning your new eSIM. I don't know how much if any benefit that would give you.
Hopefully there are other smart people here who can provide more details!