How can I check if map has some spells disabled?

Recently I played some player-made map downloaded from one of those heroes-3-maps websites. To my frustration I found out that some spells are disabled on that map - I've tried to get Town Portal but even with Tome of Earth it wasn't available to my hero. And that's not fun to defend multiple towns from random AI attacks on extra large map without Town Portal.

Is there way to check map for disabled spells before actually playing it?

Only in the map editor, if you can open the map in it (h3maped.exe, h3hota_maped.exe etc, depending on what game version or mod you have). There you have the "Tools" panel, inside of it you have the "Map specifications.." selection, and in there you will find the tab "Spells". Any spells in that list that do not have a check mark next to them will never appear in the game.

Obviously you can also change things in the map editor, but it won't be the same experience. In your case, if you just want to have single-player fun, you could consider activating those spells and saving the map. Please keep in mind that if you want to save the map with a different name then you have to change the filename AND ALSO the Map Name selection in "Tools"->"Map Specifications.."->"General". You find the map inside the game via the name in Map Name, no matter what filename you gave it.

If you can not open the map in the map editor I do not know of an other way of checking the active spells for that particular map.