1. We usually use "much" with negatives in our everyday and usual language.
"She doesn't have much free time."
A - Do you have a lot of free time right now?
B - No, not much.
C.Do you like ice cream? Yes, very much. 'very' is used for emphasis.
"She has much free time." - This doesn't sound very natural, though I suppose it would be grammatically correct. I might think it "okay" for emphasis in the right context.
She has MUCH free time.
2.We use "a lot" regularly with either a negative or an affirmative statement.
"She has a lot of free time."
"She doesn't have a lot of free time."
We also use "much" with the adverbs "too" and "so" in an affirmative or negative statement. Of course, we have to take into consideration how the meaning is affected.
"She has too much free time now."
"She doesn't have too much free time these days."
"She has so much free time now."
"She doesn't have so much free time anymore."
We usually use "much" with negatives in our everyday and usual language. However, there would be and are times when "much" is used in an affirmative statement. The usage note explains this very well.
adj : (quantifier used with mass nouns) great in quantity or degree or extent; "not much rain"; "much affection"; "much grain is in storage" [syn: much(a)] [ant: little(a)] n : a great amount or extent; "they did much for humanity" adv 1: to a great degree or extent; "she's much better now" 2: very; "he was much annoyed" 3: to a very great degree or extent; "we enjoyed ourselves very much"; "she was very much interested"; "this would help a great deal" [syn: a lot, a good deal, a great deal, very much] 4: (degree adverb used before a noun phrase) for all practical purposes but not completely; "much the same thing happened every time" [syn: practically] 5: frequently or in great quantities; "I don't drink much"; "I don't travel much" [syn: a great deal, often]