Could I attack myself with sengir vampire, block with a creature, and get a +1/+1 counter on it
No, because the rules specifically say that you attack the other player in a two-player game, or opponents in a multiplayer game. There are no cards which change this.
Here are the full relevant rules:
506.2. During the combat phase, the active player is the attacking player; creatures that player controls may attack. During the combat phase of a two-player game, the nonactive player is the defending player; that player and planeswalkers he or she controls may be attacked.
506.2a During the combat phase of a multiplayer game, there may be one or more defending players, depending on the variant being played and the options chosen for it. Unless all the attacking player’s opponents automatically become defending players during the combat phase, the attacking player chooses one of his or her opponents as a turn-based action during the beginning of combat step. (Note that the choice may be dictated by the variant being played or the options chosen for it.) That player becomes the defending player. See rule 802, “Attack Multiple Players Option,” rule 803, “Attack Left and Attack Right Options,” and rule 809, “Emperor Variant.”
802.1. Some multiplayer games allow the active player to attack multiple other players. If this option is used, a player can also choose to attack only one player during a particular combat.
802.2. As the combat phase starts, the attacking player doesn’t choose an opponent to become the defending player. Instead, all the attacking player’s opponents are defending players during the combat phase.
(There are additional rules for multiplayer variants where there are restrictions on who you can attack, but rather than quoting absolutely everything, I'll just reiterate that nothing ever says you can attack yourself.)
If you were to Donate your Sengir Vampire, your opponent would gain control of it. If you then activate Mindslaver you'll control that player's next turn. You can then attack yourself from your opponent's side of the board and block with any number of flying or reach creatures like tokens from Call. Then the vampire will gain those +1/+1 counters. On your turn you can then use Control Magic style effects to bring it back under your control and swing with your 7/7 flying. Hurray!
Or, you could just cast Give and call it good.