" i dont have any skipping on the cassette even with the older chain." That is expected, as chains and cassettes wear together. If the chain is allowed to become too worn, the corresponding wear on the cassette will make it skip when a new chain is installed. If this happens a new cassette is needed.

You should not expect to be able to judge the state of wear of a cassette by eye; its performance with a new chain will dictate whether it needs replacement. Get yourself a good steel rule and use that to check the state of chain wear; the so-called "chain checkers" are generally misleading.

As I suggested earlier, change out your chain and then see how it works. You will have saved yourself some pointless troubleshooting if the "chain drop" problem goes away with a new chain.

I'd suggest that you get a chain which connects with a master link as opposed to the Shimano chains which require the special connecting pin. The link can be opened for cleaning or other work much more easily and you do not need a new pin each time.