cb0329, 
 
jcase's app installs a custom recovery partition on your phone. Then, the step of flashing the rootme.zip or the custom rooted ROM is what actually gives you root. The rootme.zip does this by installing the su program and SuperUser app on your phone. A custom ROM (should) already have the su program on it and should also have the SuperUser app on it too. So, you gain root access/capability after flashing one of these items.
 
Regarding your ROM backup question, you could (and probably should) make a Nandroid backup of your phone prior to flashing anything. So, when you enter the custom recovery and before you flash either the rootme.zip or a custom ROM, select "Backup/Restore" from Amon_RA's custom recovery menu, then select "Nand Backup". This will make a backup of phone and allow you to restore it to its native state (excepting the presence of the custom recovery partition) should the need arise. BTW, there are excellent instructions and diagrams of this backup in erisuser1's thread 
http://androidforums.com/eris-all-things-root/127861-universal-eris-root-dummies.html#post1186824, specifically figures 33 - 37.
 
By the way, its always a good idea to make a Nandroid backup before you do anything scary to your phone (like flashing something, deleting system apps, etc.).
 
Also, make sure that you do the wipes that are required (check the dev's ROM thread) before flashing a custom ROM. The Froyo ROMs in particular since they often require a wipe of Dalvik-cache in addition to the "Wipe data/factory reset"
 
As far as the app backups go, lots of folks use Titanium Backup Pro. The paid (Pro) version will apparently backup both your apps and their data. Search the forums for more information regarding this (I don't have that many apps, so its not so much an issue for me and I don't mind doing it manually). There should not be compatibility issues, but you might want tho check the various threads on the various Froyo ROMs to see if folks have reported any issue.
 
Hope that helps...cheers!
 
P.S. welcome to the AndroidForums!