Do you go to your bed (if any) on re-spawn or are you completely relocated?

If you slept in a bed before you died, the bed still exists, and there is enough space on it for you to respawn, you will respawn there. Otherwise you will respawn at your initial spawn point. Dying from lava doesn't change this.

When you die, you have three options of respawn:

1. You got bed placed in somewhere, with enough space (1 block : BlockBedBlock) and you have sleep, and you don't removed it before die --> Respawn in Bed
2. You got bed placed in somewhere, with enough space (1 block : BlockBedBlock) and you have sleep, but you have removed it before die and placed again wihtout sleep - -> Respawn in "original point of respawn"
3. You don't have bed --> you respawn in the "original point of respawn"

Yes,as long as you have slept in it. If you haven't slept in the bed then you will be at your original spawn.

You can only respawn in your bed if you have Slept in the bed and if there is at least 3 blocks of space between your bed and cealing/ roof but it's better to have more space between the two just to be sure you'll spawn back in your house/ on your bed.