I usually improvise with the quantities, but these are all the ingredients, approximated. I looked at a couple recipes on the web for a reality check. I prefer a richer version of this than some people, so I add coconut cream near the end. It can be omitted.
You also asked about the life of the preserved rinds: I usually wait at least a month before using them and keep them in the refrigerator for as long as it takes to use them up. I've used preserved lemons that were well over a year old; as long as they're covered with brine they'll last.
Tom Kha Gai
1 cup good, strong chicken broth (not stock)
1 can (14-oz, about) coconut milk
6 slices fresh galangal (double for dried or frozen)
2 stalks lemon grass, bottom third, sliced on diagonal and bruised (double for frozen)
5-6 kaffir/makrout lime leaves, torn but not in small pieces (I dont like to eat these) or preserved rind of half a lime or grated rind of half a fresh lime
2-3 tablespoons fish sauce
1 tablespoon sugar
3-6 whole birds eye chilies, I use frozen youd probably use fewer with fresh (canned are nasty)
1 large boneless chicken breast, sliced, or equivalent (boneless thighs are good)
1 can whole straw mushrooms, rinsed a few times to get rid of the tinny flavor
About ½ cup coconut cream (not the sweetened kind)
Handful of cilantro on the stem
Put broth and coconut milk in a medium saucepan with galangal, lemon grass, lime, fish sauce, sugar, and chilies. Bring to a boil, taste for seasonings and add more of things at this stage rather than later. Add chicken. Simmer until chicken is tender. Add straw mushrooms, cook long enough to heat them up. Add coconut cream to desired thickness. Throw in cilantro and cook a little longer until wilted.
I usually take the woody stuff out before serving.
Enjoy. I hope.