1. Less - fewer
There are less people than yesterday. No!
There are fewer people than yesterday. Yes!
She ate fewer than him the buffet. No!
She ate less than him at the buffet. Yes!
Less means a smaller amount or "not as much" and is used when describing a singular or unaccountable noun.
Fewer is defined as not as much and is used when describing a plural or accountable nouns.
2. Me – I
They gave it to him and I. No!
They gave it to him and me. Yes!
He and me all going out to eat. No!
He and I are going out to eat. Yes!
Me is an object pronoun.
I is a subject pronoun.
Remember this tip: remove "him and". Does the sentence still make sense?!