两者都表示多但many后用可数名词复数
much后用不可数名词,还可修饰比较级
a lot 当然不是名词性短语了,而是副词性短语,修饰动词.比如：Thanks a lot.= Thanks very much.
再比如：I know him a lot.
plenty of 和以上lots of 和a lot of相似,后面接可数名词和不可数名词均可,接可数名词时谓语用复数,接不可数名词时,谓语用单数.
至于你说的“many, much 用于疑问句和否定句中,a lot of 用于肯定句中”是错误的,没有这规律