As the reply above says it takes a bit of storage to run a node. Storage isn't free, so I think the answer is basically no.
Yeah. Its a no.
Do you mind me asking why you want to setup a node? Is it for processing payments? There's other ways to go about that if that's the case.
A full node helps the network and its basically the backbone of Bitcoin. Full nodes are basically operating with 0 trusts on others and they are the best for protecting your own privacy. You can of course, use SPV clients like Electrum to process payments but its not exactly the most secure client out there for huge merchants.
It's just a weird request. If you want to help the network that's great, but it's either a VPS or one's PC. OP specifically asked to not use his PC but also wants free... So not even a Raspberry PI is what he's looking for.
Hard to suggest something with out more information IMO.