I have an iMac Power PC G5, OS X, version 10.5.8
I am running into problems of installing programs, downloads and even Mac OS X Snow Leopard, because they are requiring an Intel processor. I do not know if Intel can even be installed. Is it possible to install Intel on my iMac?
No. The entire Intel logic board is different from a PowerPC board. I'm sure it could be "whacked and hacked" into working but you would have invested hundreds of dollars into a machine that now looks like it was attacked by love-lorn squirrels carrying jackhammers. It's simply not cost-effective.
Check the Apple Stores Refurb section. I bought a 27" Mid 2010 quad-core i7 late last years an it was much less than a new Mac, yet still has a one-year warrantty and qualifies for AppleCare extended coverage.
Here's the link to refurbed iMacs:
Check it often---some models only stay up a short time.