Key

After buying a global IP and setting up a correct port forwarding on a router all works fine. Thanks for help.

-ModMaker- yep, i already tried this sort of thing. Nothing changed. I think it's because of my router's local IP (looks like global IPs on both sides are necessary for directplay7 games) , I think buying the global IP option from my provider should solve my problems. I'll try this out soon.
Jarno Mikkola we tried with fully clear bg1 installations it just stuck forever on the loading screen after the client press join button.

Ouch.
Well, it's not working neither in fullscreen nor in window.
Just installed 1.10 without mods - exactly same result.
I am frustrated.

-ModMaker-
Да, именно в неё родимую. Я подключен через роутер, на роутере серый айпи. У друга выделенка (билайн), белый динамический айпи, авторизация через впн. После того как впн поднимаем, пинги идут, тут все хорошо. Единственное, может порт форвардин помочь на роутере, но хз какие порты бг юзает, к тому же связь-то какая-никакая явно есть, иначе пароль бы не запрашивало. Попробуем сейчас сами собрать, может выйдет чего.

I am connected through the router, both my and my routers IPs are local, my friend connected to the provider directly and have dynamic global IP. After establishing a VPN connection between us we can see each other, ping is alright, there are no problems here. Maybe port forwarding on router can help, but I don't know which ports do BG use. Besides it if the port was closed, the game will be unable to check are the password enabled/disabled on the other side, so I doubt that it's a routers fault.

the bigg
You was right about windowed mode, but enabling fullscreen on both sides didn't help. =(