Q: Where can i get a free system update to at least mac os x 10.7 so i can communicate between my IBOOK G3 system and itunes ?? Or am i stuck until i can afford to purchase all of the necessary updates of mac os x 10.4.11up to 10.7?? to mac os x 10.7

iBooks don't support Snow Leopard or Lion, so you can't get the App Store on it, it's too old.

The G3 cannot be updated to any Mac OS X version beyond where you are now...the versions that provide access to iBooks (Mac OS X 10.9 and 10.10) require an Intel processor.  If you want access to the Mac App Store and to the iBook store you will have to buy a model that has at least an Intel Core 2 Duo, i3, i5, i7, or Xeon processor and that meets the additional requirements given in http://support.apple.com/kb/HT5842

Should you have been misled about the capabilities of the iBook G3

portable PowerPC-based Apple computer you bought online, you may

be able to return it; misrepresented products may be returned if you

bought through such places as eBay, etc.

Also, the name iBook has been re-used, it currently not only applies to

old vintage or obsolete Apple portable PowerPC G3/G4 computers, it

also applies to the newer iBooks ebooks, applications, software, and an

author application where later spec computer or device systems are

needed to utilize their function. But not current portable computers.

For relatively inexpensive Intel-based white polycarbonate Apple portable

computers that could run Snow Leopard 10.6.8 or Lion 10.7, you may find

some resellers of repaired or used stocks, with Core2Duo processors,

and these MacBook entry-level models replaced the PowerBook/iBook G4

builds in 2006, then were discontinued by 2010. Now there are MacBook/Air

MacBook/Pro models, the latest models are rather different in build & OS X.

everymac.com has information about most all Macs, including portables

and their years of manufacture, specification, and other details.

So, I'd check into the returns situation, and get some model of more recent

build; even a repaired one with a limited guarantee could be OK. Depending

on what your expectations are, you may find a deal, or a disappointment in

trying to find a bargain without  more information on what their limits are.

Older models no longer made appear in online resale sites, some companies

repair and resell a variety and their inventory is changing all the time. But other

resellers may not really know anything at all about the items they sell on ebay.

A local Mac user group may be helpful with locating something nearby. Or you

could try some online resellers who have a good reputation among Mac users.

In any event...

Good luck & happy computing!