In the future, please post only one question per thread - otherwise it can get too confusing.

1) Usage of "neither,nor", "either, or" - when would the verb be plural?

This is not a grammar topic that the GMAT actively tests. But, in case it were to come up, the rule is:

The verb will agree with the subject nearest to it.
Either the cat or the dogs are coming with us.
Either the dogs or the cat is coming with us.

2) Are these sentences correct?
- only 1% of the group has
- only 1% of the students have
- one of the spiders that eat

Yes, when we're using percents, the verb will agree with what we're taking the percent of (either "group" or "students" in this case). In the 3rd example, "that eat" is a subordinate clause modifying "spiders," so that works.

3) What can "these" modify?

This question is rather vague. "These" is generally used to refer to something in close proximity ("these pens in my hand"). Was there a specific usage you were wondering about?

4) In which cases can we use "to which", "to who"?

"To which" is used to modify nouns in constructions that use the preposition "to."
I am pointing to an object. The object to which I am pointing is a pen.

"To who" is never acceptable. The correct format is "to whom":
The woman to whom the award was given is a distinguished scientist.

This is not a rule actively tested on the GMAT.