I've got a very simple question, is it possible to transfer funds from Shelly to Byron or Byron to Shelley Wallets? If it's possible, do I need to consider anything else different than sending as usual between two Shelley Wallets?
No, transactions where the destination address is a Byron era address are no longer valid. I think you can send funds in Byron era addresses to Shelley addresses.
If you still have a Byron era wallet I highly recommend that you upgrade it to Shelley sooner rather than later. At least in the Daedalus wallet, this is trivial.
Turns out that the answer I gave above is actually incorrect. The following is from my IOG colleague Sam Leathers.
Byron addresses are just as valid as Shelley in the ledger, although have a slightly larger minutxo because of their size. A number of large exchanges still only use Byron addresses. Its probably not a good idea but it is valid.