1. a. This can be "simple calling" or "calling on the telephone"
b. As you said, this is just calling someone on the telephone.
c. This is not asking someone on a date. This is "asking someone to come outside", it can also be "calling someone to come" to another place. For example:
I called her out into the kitchen means I shouted at her asking her to come to the kitchen.
2. I can't personally think of any difference, other than the fact that "help out" sounds much more informal. Also, "help" can be used as a noun, whereas "help out" cannot.
3. In that sentence, you can use the word "omit". You cannot use the phrase "drop out" in this context, and I don't think I have heard of the phrase "drop up" before, so that cannot be used either.
Other phrasal verbs meaning "drop" and "omit" include leave out and miss out.