I have just installed a 1TB hard drive via USB onto my ps3 as im running out of room. When i install a new game a warning comes up saying i have x amount of room left. Is it possible to install the new game data onto the hard drive?

you can save games onto a USB. but downloading demos and other stuff will burn your memory so if you have alot of those you should deleter them. or delete games that you never play anymore. and if you have a crap load of accounts it will make the memory get low.

No see that would defeat the purpose of downloading to the hard drive, the reason you download some files to the hard drive is because a hard drive is faster then a blu ray disc so if you have it through usb well usb is slower so it would slow it down, i would just back up your ps3 onto the external hard drive and buy a new bigger hard drive and put the data on that throught the external harddrive