Lava Golem is a Yu-Gi-Oh card worth around $2.00
Lava+Life
No, because there is no Lava Golem in Pokemon. Perhaps you meant just Golem in general? If that's the case, it depends on the levels and Magmar's moveset.
In either of your own main phases, you can special summon lava golem. Rather than offering the cost from your own side of the field, Lava Golem says to use the opponent's monsters. So you send the opponent's two monsters to the graveyard and place Lava Golem on their side of the field. Either player can try to negate it, in which case it will be destroyed and go to your graveyard.
AROUND $2
No part of Lava Golem's text forbids it from being used as tribute. You can tribute it exactly the same as your usual monsters.
protect
Yes, Lava Golem only requires Blue-Eyes Shining Dragon as a tribute. Lava Golem does not specifically target Blue-Eyes Shining Dragon nor is it an actual effect. Therefore, Blue-Eyes Shining Dragon cannot activate its effect where it negates and destroys cards that designates it as a target.
cold lava
Yes. An opponent's Obelisk or Ra can be tributed as cost for your Lava Golem. It is not an effect, nor does it target, which is why Obelisk is not protected from it. Ra has no protections anyway apart from during his summon.
Lava Golem's own special summon effect can only special summon itself to the opponent's side of the field. Like other 'can only be special summoned by..' monsters, if you summon it correctly, and it is then destroyed, it can be brought back to the field by cards like Monster Reborn. In Lava Golem's case, it will be special summoned to your side of the field if you do this.
no it can't unless you have a lot sleep, stun or blast seeds