Variant of MerkleTree with dynamic height?

Question

Algorithms

Is there some sort of hashing algorithm that allows you to add and remove elements dynamically, and check if an element is in the chain?
Something similar to a Merkle tree, but which is built dynamically and for which you do not need to have all the values

Root1 = Hash(Value1);
Root2 = Hash(Root1 + Value2);
Root3 = Hash(Root2 + Value3);
Root4 = Hash(Root3 + Value4);

That is, at the output we have the height of the hash (In our case 4), the root hash (In our case Root4) and the value whose occurrence must be recursively checked in this chain (In our case Value2)
Root4->Exist(Value2)
And the second very important point. Is it possible to remove values ​​from the chain.
Root3 = Root4->Remove(Value1)

Answer 1

Is there some sort of hashing algorithm that allows you to add and remove elements dynamically, and check if an element is in the chain?

The Bloom Filter is perhaps the most effective, but false positives are possible.