aldric, luis, aldrin = etymology?

hello, good morning!

great masters of the tongue, i have questions that need wisdom:

1. regarding the etymology of the germanic masculine name:
*aldric/aldrick; eng. *aldrich. i think the name means "old-ruler"
right?! what is the latinised form of the germanic "aldric?" i'm
guessing it's *aldrico or *aldricus. furthermore, what is the latin
equivalent? *altus rex? doesn't sound like a catchy name.... help!
correct me if i've been mistaken please.
2. regarding the etymology and origins of the modern spanish name
*luis and modern french *louis. i've heard it came from the frankish
name *clovis, but i also heard it was from the latin *ludovicus. are
they cognates?
also:
is the german *ludwig cognate to the latin *ludovicus? and thus to
*luis/louis? again, help please.
3. regarding the etymology and origins (again) of the name *aldrin.
i'm clueless, actually. all i can think of is the "alder (tree.)"
could this name be cognate with the tree's? possibly meaning "of the
alder" (alder+in) like "oaken" = "of the oak" ??? big help on this one.

may this thirst be quenched.

thank you very much.
PHIL