Are same-sex marriages allowed?

The Unofficial Elder Scrolls Pages States that:

In Skyrim, you have the option of marrying an NPC, regardless of race or gender. To do so, you must complete the quest The Bonds of Matrimony, which involves speaking with Maramal about marriage and wearing an Amulet of Mara which signifies that you are available to be married. Once you have found an NPC who also wishes to be married, and whose disposition towards you is high enough, you can gain their consent to marry you and then attend the wedding ceremony at the Temple of Mara. After the wedding, if you speak with your new spouse, you can determine where they will live.

As long as you want to marry an NPC that wants to be married, regardless of race or gender, you can marry them. So, interracial marrying is also possible.

Yes it is possible. Additionally, if you see an NPC you like but can't marry him/her, you can use a console command that changes their status.

I think this is the command: Addfac <variable> 1 - Adds the selected NPC to a faction (e.g. addfac 19809 1 adds an NPC to the marriage-faction, allowing players to marry this NPC)

Note: Be very careful when using this command. If you use it on an important NPC it can break any quests related to that character.

Same sex marriage is allowed in the game.