I used to do a lot of mischieves when I was Jonathan's age. Who is five at the moment.

I used to get up to a lot of mischief when I was Jonathan's age, which is five.

I used to get up to a lot of mischief when I was the same age as Jonathan, who is five.

So we cannot say "he does a lot of mischief". We need to say "every day he gets up to a lot of mischief that gives us headache". It should always be preceded by "get up to" am I correct?

Mischief is an uncountable (mass) noun. Children do a lot of mischievous things, or "get up to" a lot of mischief. This is using mischief in the sense of harmless childish playful actions. We say 'do mischief' to mean actual deliberate harmful damage mainly by adults.

"Every day he gets up to a lot of mischief that gives us headache". Is this sentence correct?

Okay so we can say "children get up to a lot of mischief" but if we say "he does a lot of mischief" so it means we are talking about an adult who deliberately tries to harm other with his mischievous things. Am I correct?