My question is, what cards can be used to protect it?
Perhaps the most adequate card for your purpose would be Field Barrier (emphasis mine):
Field Spell Cards on the field cannot be destroyed. Neither player can activate a new Field Spell Card. You can only control 1 "Field Barrier".
That way, your opponent would have to destroy Field Barrier first, and then attempt to destroy Salamangreat Sanctuary. This will have to be in two, separate attempts, as activating a global destruction (like a Great Storm, say) would save the Field as it is simultaneous destruction (moment in which Field Barrier still saves it).
The only downfall is that it does not prevent Salamangreat Sanctuary from things like returning to hand (as it does not destroy). One card that could bypass Field Barrier could be Murmur of the Forest, for example... but using Field Barrier already gives you a great advantage.
And is there any Salamangreat monster that can protect it with its effect?
Most likely, the reason why only one field spell card is used is because Salamangreat Falco can recover your field spell card (emphasis mine):
If this card is sent to the GY: You can target 1 "Salamangreat" Spell/Trap in your GY; Set that target to your field. If this card is in your GY: You can target 1 "Salamangreat" monster you control, except "Salamangreat Falco"; return that monster to the hand, and if you do, Special Summon this card. You can only use 1 "Salamangreat Falco" effect per turn, and only once that turn.
So most likely meta Salamangreat decks rely on using 3 copies of Falco, which can recover your Field Spell card when sent to the GY (like, when you link summon, for example).
You can then bring Falco back to the field, send it to the GY again, and recover another Spell/Trap card.