yes, you can remove and upgrade to better. you can sell the old upgrades that you don't want or need anymore.
blank rune stones can be purchase from several merchants in the game.
you get the recipies/schematics from quests/missions and exploration, and a couple of recipies and rune stones {i think} as rewards for war room missions.
if a weapon already has a rune stone in it, it cannot be removed, but it can be replaced with another, which destroys the one already on it.
once you have the recipies, you'll need the elemental essences from kiiling diffrent fade rift creatures... spirit essence, fire essence, ice essence, lyrium essence, etc. All of which, iirc, have different levels of potency... i think there are 3 or 4 tiers for each. basic through pure.... pure being the best and most potent.