1. Violence on television is more of a recent problem.

(What other similar expressions can we use instead of 'more of'? Do you use 'more o' often?)

2. There is only so much (that)you can read in magazines and newspapers.
(Can we insert 'that' in this sentence? What is the part of speech of 'that'? What is the meaning of 'only so much' here?)

Instead of "more of" --

-- is a rather recent problem.
-- is something of a recent problem.
-- is a somewhat recent problem.

Yes, you can either keep "that" in the second sentence or omit it. If you keep it, it seems to be serving as a relative pronoun, referring to "much" (modified by "so").

In this sentence, "only so much" means that people can get a certain amount of information from magazines and newspapers, but the phrasing implies that people can get even more information from other sources.

#1 You could just say that violence on TV is a recent problem. "more of" does not mean more often. It implies that violence on TV is a greater problem now than in the past. "more of" means larger or greater, although the frequency of the depiction of violence (more often)may be inferred.

#2. "that" is a pronoun, in this case something understood, as in the reading material available in magazines and newspapers. It is not necessary in this sentence, since it does specify magazines and newspapers, but is quite acceptable.

1. Instead of using "more of," you can replace it with similar expressions such as "increasingly," "becoming more," or "growing as." The phrase "more of" is used to indicate a greater amount or degree of something, and it is commonly used in casual speech. However, it may not be considered formal or grammatically precise in all contexts. It is always advisable to use a variety of expressions to enhance your language skills.

2. Yes, you can insert "that" in the sentence: "There is only so much that you can read in magazines and newspapers." In this case, "that" is a pronoun, functioning as the direct object of the verb "can read." It refers back to the idea of the limit or extent of what can be read in magazines and newspapers. The phrase "only so much" suggests a limitation or constraint, meaning that there is a finite amount or limit to what can be read in those sources.