"Information" is usually* uncountable in English (although the equivalent word may be countable in other languages).
The adjective "various" is generally used to modify countable nouns, not uncountable nouns, so it is not usually appropriate to say "various information"--unless "information" is acting as a noun adjunct.
At present, most users, at least in the US, would use "various kinds of information" or "various types of information" rather than "various information" for this reason.
However, there may be regional and historical differences in the usage of "various information."
A search of the Corpus of Historical American English finds 11 uses of the phrase "various information" from 1820 through 1995. "Information" acts as a noun adjunct in only 2 of the 11 cases. By contrast, a search of the Corpus of Contemporary American English finds 12 uses of "various information" from 1990 through 2015. In all of these cases, "information" is acting as an noun adjunct (examples: "various information gathering processes," "various information formats," "various information sources," "various information technology firms"). This suggests that there has been a shift away from using "various information" except as a noun adjunct over the years.
A search of the Hansard Corpus, covering proceedings of the British Parliament from 1803 through 2005, finds that from 1810 through 1939, "information" was never used in that phrase as a noun adjunct. However, from 1940 through 1990, "information" was used as a noun adjunct in roughly half of the uses, with the proportion increasing in the latter years. No instances of the use of the phrase appear in the Corpus from 2000 through 2005.
A search of the British National Corpus, covering the 1980s and early 1990s, finds 5 uses of "various information." In 4 of the 5, "information" acts as a noun adjunct.
*Oxford Living Dictionaries indicates that "information" may be used in legal jargon as a countable noun. Examples provided with this definition at that source include:
- ‘the tenant may lay an information against his landlord’
- ‘However, the duty of the court is to hear informations which are properly before it.’
- ‘These private informations came before the Justice of the Peace for the pre-hearing required under Section 507.1 of the Criminal Code.’
- ‘When the justices purported to commit the appellant on these informations, they were doing something which in law they had no power to do.’
This use of "information" appears to also occur in law in the US (for example: "The order of the Appellate Term should be reversed, and the informations dismissed"--from a New York State appellate court ruling in 2003).