No, for two reasons.
If it doesn't say "deal(s) damage", it doesn't deal damage.
It's only damage if it's the result of the "deal damage" keyword action. That means those words must appear in the rule or effect. Currently the only damage caused by the rules is combat damage. So if it's not combat damage, and if the effect doesn't use the words "deal damage", it's not damage.
In the Combat Damage Step, attacking and defending creatures deal damage. If any of that damage is directed to you, it will be nullified. You won't lose life (or gain poison counters if the attacking creature has Poison or Infect) if you don't block an attacking creature because you are protected from the damage that would cause you to lose life (or gain poison counters).
A Lightning Bolt targeting you will have no effect.
"You" refers specifically to the player.
Personal Sanctuary only protects you from damage. Your permanents are not protected.
No, "prevent all damage" only prevents actual damage - the kind of thing that happens when a creature deals combat damage to you, or a spell or ability deals damage (it'll actually say "damage", like "Lightning Strike deals 3 damage to target creature or player").
Firstly Personal Sanctuary only protects you not your permanents.
Nope the the only time a damage prevention effect can save a land is when the land is also a creature (weird but it sometimes happens) and is actually assigned damage from a spell, ability or another creature.
Similarly damage prevention doesn't work against effects that say 'lose life' (this phrase is used on effects that affect a player) or destroy creatures outright. So for example Personal Sanctuary won't protect you against some thing like Absorb Vie.