Hello there! All these mini games on telegram are accessible only through the telegram interface, I don't think they can be opened in other places.
Regarding the connection, you do need internet, but I don’t think it requires particularly fast bandwidth to function properly. Also it is not an online in real time game like COD or similar, you play versus bot, or you can compete vs other players but it is all automatic.

I mentioned the "pay to earn" aspect because, like many other games, you can buy upgrades that help you achieve higher scores in a shorter amount of time. I see it as an alternative to constantly playing: if you want to "bet" on the game rather than playing and leveling up more slowly, you can opt for these upgrades and level up faster. However, this won't give you direct monetary gains, but it will allow you to position yourself better and more quickly to receive a larger share of the upcoming airdrop.
This is, of course, optional: I personally haven't bought any packages and I just play a bit in my free time.

You can try it, it's free! 😊