(Not a Teacher)
"I have many friends." "I have lots of friends." -- Both of these sentences are fine.
"Many" is typically used with countable nouns. (Such as people, apples, trucks, sandwiches, doorknobs, and other things that can be quantified in definite terms)
"Much" is generally used with uncountable nouns. (Such as sand, sugar, water, sarcasm, liquid soap, time, and other things that are hard to quantify)
Whether a sentence is positive or negative has nothing to do with when "many" and "much" are used. Their usage is wholly dependent on the noun they describe.