It's still really early days - it can take a few months for new cats to find their place in the pecking order!
Feliway can really help, but it's a bit pricey as you may need more than one diffuser - I think they're about £20 each.
Playing with them (one of the stick and string toys is ideal) at the same time is also great for bonding.
The normal relationship to expect is actually that they just ignore each other, it's very rare to get two non related cats curl up together as you described. I have four, all moved in at separate times, and all took at least a couple of months to settle. None of them will sit together but there's very little fighting now.
Make sure you have plenty of litter trays (one per cat plus one is the normal guideline) to help stop any spraying, and give them time.
I have two 9 year old cats (brothers) and recently agreed to foster a 10 year old cat. He came last night.
Previously a couple of cats have adopted our household - one was accepted by my cats and whilst they all did occasionally play fight they used to curl up together and lick each others faces. The other was very skittish and vicious and used to run away with my cats or attack them and it caused one of my cats to start peeing everywhere. I am keen to have the new cat be mpre like the former experience.
So far the new cat has mainly just sat on our bed and when one of my cats has hoved into view there has been ears back and hissing - but no attacking.