Assumption 1: Existence has a cause(Causality)
Better assumption imho: Everything that exists has a cause (because that is what you use in your proof). You don't need to mention existence itself, it never comes up in your proof.
Assumption 2: Causality exists
Note that your "exists" here seems like it is not just physical existence, but metaphysical existence of concepts too (so, there is a cause for the existence of numbers according to your assumptions?!)
Because causality exists, there is a cause for causality to exist.
Fine
The cause of the existence of causality is also causality.
Questionable, and follows from nothing. We have established what causality means, but not that it causes anything. There is a cause for causality, according to your assumptions, but it's not necessarily causality itself. The fact that something causes causality is also causality.
("existence has a cause" do exist(Assumption 1,2) because existence
has a cause)
Therefore, the cause of causality is causality.
This is circular logic.
Therefore, the assumption must be denied
Circular logic is not a contradiction. It just means you failed to prove anything, the statement as well as its negation. It's like in math when you transform equations to solve them, but in the end only end up with the original one. You didn't prove or disprove something, you simply failed in your proving process. In any case, you have two assumptions that are important to your proof, so even if you had a contradiction, there are three possible scenarios that might be true:
Assumption 1 is wrong (your version of Existence has no cause, or alternatively not everything that exists has a cause, but causality still exists)
Assumption 2 is wrong (Causality doesn't exist, but your version of existence still has a cause)
Assumption 1 and 2 are wrong (your version of Existence has no cause and causality also doesn't exist)