Is it grammatically correct to use a colon after an incomplete sentence? Is it correct to use it after the word "because"?

We have two questions posed here so let's take them one at a time.

Is it grammatically correct to use a colon after an incomplete sentence?

I'm not sure what is meant with this part of the question. An incomplete sentence is one that is missing a verb or an object the verb is missing, for example:

The wet brown dog on a leash down by the river.

So having a colon follow this would not be appropriate:

The wet brown dog on a leash down by the river:

The second part of the question asks about a colon following the word "because". Where there is a list of things related to the "because", a colon will absolutely work:

The wet brown dog on a leash down by the river was wet because: it wanted to chase ducks, it wanted to catch fish, and it was having fun playing in the water.

It'd be hard to put the two parts of the question together because a list isn't going to provide verbs for the incomplete sentence. I can't say:

The wet brown dog on a leash down by the river: is running after ducks, is trying to catch fish, and is barking in excitement.