Suppose I have Merkle Tree with Transactions 'A','B','C','D','E','F' and I want to know how to check if particular transaction i.e 'A' exists in a Tree or not ?. And if it is present then how to traverse using root hash to the node with transaction 'A' ?
A Merkle tree is just a particular way of hashing a list of elements. In this application, the elements are transactions.
Finding something in a Merkle tree is just looking through the list. The Merkle structure does not help you.
However, what you can do with a Merkle tree is create a compact proof that a particular element is included (by giving the hashes higher up in the tree it is combined with).
So to summarize: you don't use a Merkle tree for searching. You use it to prove things are in it. This means the searching can be outsourced: if some (software) party tells you about a piece of data that allegedly belongs to a tree, instead of checking it for yourself (which requires having the tree), you can ask for a proof (which can be verified by only having the root).