Happy New Year! It does seem like the more you learn, the more questions you have, but that's why we are here, we love questions!
Your English is excellent! I would have never known you were not a native speaker if you hadn't said something
Your steps look correct to me, I think you are ready!
a) For adprep, two questions for you. What operating system is your current DC running? How big is your AD database (ntds.dit)? According to Microsoft, if your database is larger than 100GB, adprep may cause high CPU utilization by LSASS and high disk utilization from the writing of indexes. This would affect your existing DC, but no impact to network performance. It would also cause additional replication traffic, but since you only have one DC currently, this wont apply to you. Assuming your database isn't nearly that large, I would probably let adprep run automatically during the promotion of the new DC. I would wait for the morning rush of logon traffic to subside, ensure that the VPN is connected and you can ping the current DC by name, and start the process. You will be notified if there are any problems with the adprep process.
b) I would recommend using the IFM option, since you are going to the new site to set up the new DC anyway. Easy enough to create the IFM media while you are at HQ. While adprep won't generate network traffic, the initial database replication will. I think your bandwidth would be sufficient, but since IFM is so easy to do, why not?
c) You will need to create a subnet for the HQ site. When you only have one site, subnets don't matter, everything is in the only site. Once you start defining sites, you need at least one subnet object for each site. If a client has an IP address that is not part of your site design, AD won't be able to determine what site the client is in. So a client in HQ could have there logon traffic, etc sent to the DC at the branch office. You could define a catch-all subnet for HQ site, but these add unnecessary complexity and can lead to problems down the road. If you want more information on a catch-all site, let me know.
Keep me posted on your progress, and of course ask if any more questions come up!
**if the post above has answered the question, please mark the topic as solved.