'Let's play Heroes 5 online.'

It should be empty. When playing Heroes 5 over a local network, the list is not used. Create a game and play. But if you don't see the created game, that's a completely different matter.

I've played Heroes 5 over a local network several times – if you have Hamachi as your primary adapter and there are no firewalls, the list of players will display those who have joined the local (non-Ubisoft) network, provided you have joined it yourself, of course. There is a chat where you can communicate, and a separate list of servers.

15 people is the limit on the number of people in the network.

As far as I know, the limit is 24 people. If you need more, you can try Plan – but I don't know how many people can fit in a room...

I have this question: is it possible to play with three people via Hamachi?

Hamachi is a local network over the internet (Hamachi server). Draw your own conclusions