Why don’t you participate in the portal’s tournaments?

Ta Kotoraya...
Is 53.2 Kbps enough? That's the speed I have, and it's quite slow. And sorry for the dumb question, what's the difference between offline and online (I've never played either, only at home with my computer, either in a campaign or on a single computer).

Offline is, as Tamara said, when they post a starting save file. You download it and play at home, by yourself, against the computer... Then you send the final save file to the organizers. Most often, these tournaments are played for the shortest time spent by the player to complete the map. But there are also other types of tasks - accumulating experience, gathering skeletons, etc...
For offline, you only need the internet to download and send the save file. ;) So I think that's more than enough!
In general, I advise you to watch the tournaments on the forum. Read it - you'll understand what's what ;)