Edit, seems I am a bit late in my reply. I will leave it up though.
First thing to remember is that these hacked firmwares are a product of reverse engineering which is a delicate art at the best of times and things are subject to change (indeed MS may well do otherwise acceptable things as far as a stock 360 goes that trip up the efforts of the hackers), iextreme unlike many of the older firmwares also brings checks to try and keep people from not being banned from live.
Back on topic
1.6 does not have wave 4 support.
1.61 does although it is only out for Samsung and Benq drives (hitachi 1.51 unlike the other drives does support wave 4 though).
liteon drives have nothing other than the one shot boot disc at this time although a new firmware should be coming in the not too distant future.
In terms of checks though they are more or less the same (unlike earlier versions/firmwares which did not have checks) so yes playing old games is not a problem.
Edit: I sense my phrasing might confuse:
The later versions of iextreme brought more strict checks to the table so discs that might have worked on earlier firmwares might now refuse to work. The difference between 1.6 and 1.61 for the main checks (other than the support for the new style disc formats wave 4 brings) are negligible though.
To update the 360 dvd drive firmware you need to use the sata port, there is no way of using a DVD to update it.
Previously hacked firmwares will give up the keys easily though so no need for special hardware beyond the compatible sata card (no need for a probe or special measures that you might have needed the first time round).
@popopola iextreme updates are for many reasons including bug fixes, new features and support for changes to things.
Examples
1.4 brought a fix for the angles problem (see the "bad kreon rip" part of the startup page of abgx360 for more on that)
1.6 brought built in 0800 mode (used for dumping games) where before you would need to either flash the drive and flash it back or have a drive dedicated to dumping.
1.51 brought wave 3 support to the 1.5 line. 1.61 does wave 4 for the 1.6 line.
The reason wave 4 games do not work is because certain aspects of the disc were changed for the new xbox updates from microsoft (they bundle them on discs occasionally), if you want the proper tech info/explanation then
http://abgx360.net/ .
This change could in theory be the fault of a bad rip so the checks the hacked firmware does will shut it down before you can play it (it was not supposed to happen but it did).
Indeed some of the far older firmwares (of versions thereof) lack these checks and some people have gone in for them.
Note that these firmwares are not necessarily that good and they do not exist for the newer drives (namely the liteon).
I am deliberately avoiding mentioning wave patching as it is not a future proof thing and even with banned drives I suggest you wait it out (better to waste one disc on the one shot boot disc now than however many reburning stuff later).
