how do this and icicle (or popsicle!) relate?

The second c in icicle isn't there in the OE word that icicle derives from: gicel. Probably from a folk etymology based on ice.

Fascicle (or fascicule) is from Latin fasciculus. -culus (like German -chen and -lein) is really two diminutive suffixes in a row: the -cV and the -lV. Fascis (origin of the word fascist) is indead a bundle. You can see a fascis on the back of the old Mercury dime. It was a bundle of sticks around an axe. The axe was a ceremonial weapon (kind of like a mace) that Roman lictores carried. Different magistrates had the right to have different numbers of lictores carry fasces around and protect their person (and office, I suppose).