And yes I would say they are fully interchangeble

'A lot of ' has the same meaning as both 'many' or 'much', but is more informal.

I think "many" is more formal and "a lot of" is more informal

They are interchangeable,however, you should avoid using "a lot of" when you are writing essay.

LOL looks like many of these answers are incorrect. They are not interchangeable. "Many" can only be used to countable nouns. For example, He has many dogs. You can count dogs (1, 2, 3, etc.) But you can't say "He drinks many water." Water is not countable. Do you count water 1, 2, 3? (you need to use classifier here, like a drop of water, two tons of water, etc.) The word "much" can describe the uncountable nouns. "Love you so much." You don't say "Love you so many." Love is an emotion that's uncountable. Therefore, for the previous example, you can say "He drinks a lot of water." "A lot of" can be used for both countable and uncountable nouns.