Hi!
a) Lots of :
a.1. It is used before a noun.
a.2. It is informal.
a.3. I is used with uncountable and plural nouns
There is lots of water (Uncountable, therefore the verb is singular)
There are lots of people (plural noun, therefore the verb is plural)
The are lots of cars there (plural, therefore the verb is plural)
There are lots of interesting things to do in Madrid (plural.therefore is used the plural)
NOTICE: The verb must agree with the subject.
b) A lot of:
It is just more formal than "lots of". It follows the same rules as "lots of".
There is a lot of water
There are a lot of people
There are a lot of cars there
There are a lot of interesting things to do in Madrid.
- For answers: Are there a lot of cars there?. Answer: Yes, a lot. Also, you can answer "Yes, lots", but it sounds rather informal.
c)Plenty of = More than enough
There's no need to hurry. We've got plenty of time (more than enough)
We have plenty of ideas (more than enough)
There is plenty of food here (more than enough)
As you can see here, it is used with uncountables, and plural nouns.