Heat can kill some plants, but many will be ok. Unfortunately it can be difficult to predict at times due to a number of factors, from a plant's individual tolerance to its overall health.
Salt can definitely cause mass casualties of tanks, but many species are particularly resistant to brackish conditions, eg lilaeopsis sp. As above, it can be difficult to predict.
Most of you standard ich meds, eg QuICK Cure, are a combination of malachite green and formalin. In general, they are entirely plant safe, but are potentially toxic to snails/shrimp, so their should be used with extreme caution in tanks with those denizens.
In my own experience, I usually opt for chemical treatment. It's faster, very safe, and generally easier on a tank than high temps or salt from a fish perspective, as many tropical species or subtropicals really don't appreciate temps that high.