Hi,
I'm going to start with the seperating accounts. What you want for that is a reseller account. It allows you to be the admin of the accounts which you would make an individual one for each client (just like the one you use now) and you can have access to their accounts through the "reseller" username. There would be an added control panel for you to use in this called WHM (you can find some tutorials on the eUKhost support section about how to use this).
The next thing, if your server goes down, everything goes down. The only real way to get round this is to split your
web hosting over 2 servers. So you could have 2 reseller accounts on different servers. It's more work to maintain overall but it does mean if one goes down you're not dealing with all your clients going mad.
I would say if you're relatively new to
web hosting the reseller is the best option. Anything higher than that e.g. a
VPS Hosting gets more technical and moving from shared to
VPS Hosting is a steep learning curve which I found myself!