Do the words "in relation to" imply any relativism? For example: "The earth is small in relation to the Sun", or "I am good in relation to mathematics", or "He is morally bad in relation to her (with her), but not morally bad in relation to me (with me)", or "The kitchen is small in relation to the room". Is it a relativism or objectivism? Or is it just a way of specifying an objective concept to something relative?
One way to differentiate relations from properties is to differentiate between monadic and polyadic predicates. A relation is then any predicate more than one-place in its argument (input). Now relativism would then be the claim that some one-place predicate is better conceived of as at least two-place, over the "relative to" predicate itself ultimately.
In ethics, for example, we might say, "X is good," is incomplete, and we need to relativize it as, "X is good for Y," or (more in line with the common usage), "X is good according to Y," where Y is a culture, society, or some similar thing (a civilization, maybe?). "X is good only in relation to some Y," is the most general such sentiment, then.
Note that objectivity and relativity are not opposites. A chair can be to the left of something, and this is a two-place predicate; but it is not to the left of something just in case I am conscious of or believe that it is, or whatever along this line. The quasi-opposite of relativity is absoluteness (I say "quasi-" because sometimes we talk of things being absolute "for" a restricted domain, and anyway "absolute" means "in all relations," so it isn't quite contrary to "is relative to" simpliciter but a limited relativity).
Not necessarily. "in relation to" is a much more general relational concept and usually employed to clarify the two compared objects or specify some background context. It can be used in any situations when you need. Relativism is a much more restricted philosophical doctrine terminology which is usually concerned with one's morality, ethics, culture, and epistemology. Of course they both share same underlying semantic meaning of perspective dependence. For example, in philosophy of science we have a certain doctrine called "Space Relationalism", never called "Space Relativism" as it's concerned with physics not morality or culture, at least upon first glance...
Another often-heard term is "Relativity" which is a famous purely scientific physics theory thus can be validated by experiments in many ways. It further explores motion and spacetime relations under extreme speed or mass distribution conditions and somehow favors above said space relationalism doctrine in some modern improved way.