Is there a way to install and use PowerPC applications on Intel Macs?
There was an emulation layer called Rosetta to allow Intel Macs to run PowerPC applications that Apple provided from Mac OS X 10.4 to 10.6. Sadly, they removed it in 10.7 Lion and it no longer works. Given that you said your iMac is brand new, it presumably came with Lion preinstalled, and is unable to run anything older. So, unfortunately, the answer is no.

Your options are to upgrade your Adobe software to an Intel version, trade in your new Mac for a slightly older used Mac (from early 2011 or earlier) and put Snow Leopard on it, or continue to use your old hardware for your Adobe software.