Rooting won't change the speed of anything that's currently on the device, be that the browser or just the speed of the UI in general. All rooting does is give you "root" access to parts of the phone that you otherwise wouldn't be able to access. It won't change anything about the phone or device execpt for that. After you've rooted you can then go about changing things via a custom recovery through which you can install custom ROMS and kernels.
Rooting on the rezound is a fairly painless process as long as you follow the instructions and understand the risks (I'm guessing you do since you jailbroke you iPhone)
I'm not sure what the browser speeds of the prime are but the Rezound on Gingerbread is pretty dang fast being 4G and all. If you wanted to get ICS on your Rezound you would have to do the following in this order:
Unlock your bootloader through HTC's dev site
Root the phone using one of the root methods available, perm-root I think is what I used
Install a custom Recovery like Amon Ra or Clockwork Mod (I found this to be the trickier part because I'm no good with c: commands and all but follow the directions and you can muddle through it like I did)
After you have a custom recovery I would highly recommend you make a full nandroid backup in case you don't like the ROM your about to flash and you'd like to or need to get back to straight up Gingerbread
Flash the ICS ROM of you choice...as of now I think there are at least 2 ICS ROMs for the Rezound that I know of.
By doing all of this you will be voiding warranties blah blah blah but more importantly you will be performing a factory reset of the device and wiping all the data on it (not the SD card, just the internal stuff) so if there's stuff you want to save you'd better do a backup of those apps and data with Titanium Backup.
As I said, there are more detailed instructions floating around here and on XDA. Good luck.
Oh and to answer your last question, no Beats EQ will not work on ICS.
PS: Unrelated, how's Oahu? I lived in Eva Beach for 3 years...can't say I miss that part of the island though.