1. No and yes. Well, kinda :D
How most runes work is that they are actually multiplier, not a flat bonus, so if your sword goes from 4 cut damage to 6 and you have rune that increases cut damage (let's say by 25%), then yes, bonus you receive from that same rune will be higher. Rune itself won't change and item won't calculate rune any different tho.
2. Runes don't leave imprint. If you level up item and remove rune, you also lose whatever rune was providing. IF you re-roll item and get same bonus that your rune provides, then you can take rune off if it's same or lower level, as same bonus from multiple sources don't stack and only highest level of same effect works.

OK. So I can put a low-level rune into a piece of gear if I don't have any runes of a higher level with that same stat and I don't need to worry about keeping that low stat if I find a higher level rune? I can replace the low-level rune with the higher-level rune and that stat increases along with it?

Well, yes? runes are just extra passives that work while in equipment. having multiples of same rune gives no benefit and you can always remove lower level rune if you get higher level rune to replace it. It's very simple thing :D

Ah OK. Thank you. I was concerned about that so I was saving all of my runes until I could upgrade them to the highest level I could make them. Now I don't need to do that. Good to know.