Much and Many Usage
Much and many are used in negative and interrogative sentences. Much is used with non-count nouns.
Definition of "Several"
Two is a "couple" and more than two or three is several. Several is a word that shows size or number when you can’t be specific or when you want to summarize.
Much / Many with a Noun
Both can be used in interrogative and negative sentences. Much is never used in positive sentences (but we can use "very/too much"). Many can be used in affirmative sentences, but not often.
Definition of many a/an —used with a singular noun to refer to a large number of things or people. For example: "Many a tale was told."
Is "A Lot" Plural or Singular?
By extension, it means "a large number/quantity of things/people". It behaves like the noun it refers to. If that is a plural noun, a lot is plural; if there is no noun (as in your first example), a lot is singular because it means "a large amount".