1) How do I remove a road from the map? It can't be removed with the brush that paints grass; I can only replace it, for example, with an "infernal" road with ash, but that one also can't be removed.

At the bottom, on the same panel as the road, there is a button called "ERASER" (or something like that, I don't remember the exact name). Click on the road, then click on it again, and the road will be removed.

2) I don't see my map in the scenario menu after launching the game. The map is located in D:\Games\Heroes of Might and Magic V - Tribes of the East\Maps, the name is in Latin, but still...

If it's in the Multiplayer menu, are you sure you selected the Single-player scenario type when creating the map, or did you choose Multiplayer? If it's for Multiplayer, just check the "Multiplayer maps" box above the map selection menu in the single-player game.

And just a question - how do I create "gates of hell" on the ground, like in the last Necropolis mission with the capture of Holyflame, where you need to place four of your heroes?

You can download a mod that adds effects to the map editor menu, or you can add the effect manually. As a beginner, it's easier to use a mod, so click here (FullEditor). I think you'll be able to find the demon gating effect later.

Tip: read the manual; the first two questions are definitely covered there.