Using Google Mail in a mail client while being connected to a VPN server is not going to work unless Google "learns" that you travel often. It's one of Google's customer security measures to deny access to the account for possible attackers who found out your password. I've taught them that I travel to Switzerland to "work" and travel back "home" to Germany, but this works for one IP only. I can pull mail but sending it is impossible still.
For you, it's time to change the provider. Posteo from Berlin is a very good choice, ProtonMail from Zurich I think offers the same features for free. Be aware, if you don't pay for the product, you are the product.
We also have got a thread about such mail provider suggestions, since Tapatalk makes linking a difficult practice I cannot provide links at this time.
You don't have to open ports because you connect to a remote server, not the other way around.
Sent via Tapatalk. Means, I don't have a computer available now.