No difference: 'a lot of' and 'lots of' have the same meaning: they both mean a large amount or number of people or things. They are both used before countable nouns and uncountable nouns.

Yes I have found the same information but from another source.Lots of is more informal But ''a lot of'' is also informal but less informal than lots of

Lots of is more informal than a lot of, but is used in exactly the same way. https://www.ldoceonline.com/dictionary/a-lot

I'm not 100% certain, but I think "lots" is the plural form of "a lot". So whether you use "lots" or "a lot" depends on whether the word it is modifying is plural or singular. In "there is a lot of noise outside", noise is singular so "a lot" must be singular. In "there are lots of noises outside", noises is plural so "a lot" becomes "lots" (its plural form). I'm not sure if that answers your question, but I hope that helps.