Are they fallacies? what are their names?

Are they fallacies? what are their names?

1- when someone asks for proofs, data, search in every statement, even for universal concepts.

2- when someone uses general terms  to avoid speaking specifically, for example, instead of talking about homicide or safety, he talks about peace.

1- when someone asks for proofs, data, search in every statement, even for universal concepts.

I'm guessing you're referring to someone who says "source?" for just about everything, even that which is considered "obvious". 

My first thought is logic chopping but that seems to refer more to making trivial objections to a proposition in order to distract from its main point.

I get the impression, then, that rather than any specific fallacy, it's just a person being pedantic.

2- when someone uses general terms  to avoid speaking specifically, for example, instead of talking about homicide or safety, he talks about peace.

Using general terms is not always bad - it depends on what the person meant. Maybe they were making a comment about 'world peace', for example.

When fallacious, this would be considered the ambiguity fallacy.
 

I’m not sure there are logical fallacies in either example, but perhaps I don’t understand the context.

While there are probably many understandings of “logical fallacy”, I’ll go with the one on which this site is based – arguments that contain  non-factual errors  leading to fallacious reasoning .

For #1, if the person is challenging assumptions to make sure they make sense, it seems the goal is leaning toward eliminating errors in logic and fact rather than introducing them.  On the other hand, if the goal is to be able to say “You can’t give me the fact (or proof, or data), therefore none exist, therefore you are wrong!”, we now have a situation in which a logical fallacy could be in play.

For #2, if the switch to general terms is done introduce a point that really doesn’t relate to the main point of the argument, it could be an attempt to use ambiguity to distract.  For example, someone arguing that keeping any house pet should be made illegal because domestic cats that are allowed to roam free outside have a negative impact on certain bird populations would be using a general or universal ban (all pets) to address a specific issue (reduced bird population).

So, to answer your question directly … maybe, depending on the context.