If your mobile is slow try to get a task killer from play store. It will kill apps that are open in your background and are not needed. (addendum not needed! - edit)
And to answer your last question I recently had to downgrade my Xperia U from 4.0.4 to 2.3.7. It's actually easier then it sounds, the process is the same when upgrading, you just have to download a few things ;D
Remember: Flashing will delete everything on your phone so make sure you backup your mobile.
Note
Back up your phone via Sony's PC Companion Suite before proceeding
Follow the steps:
Get the following:
Flashtool, found on github
Your Xperia Firmware
Xperia U Firmware 2.3.7: found on 4shared site
(put this one in a place that is "clean" best option desktop)
Install flashtool
go to your Phone's Settings > Developer options/USB debugging (and check that option)
Connect your phone to the PC (USB)
Before you continue
Go to the folder where you installed Flashtool, open Flashtool's drivers folder and run the installer. (Flashtools\Drivers)
In that installer select your phone and click next.
WARNING:
Xperia U is next to Xperia P it is not hard to find but you can easily miss it.
After installing proceed to step 5.
Open Flashtools (click yes if anything pops up, it could take a few second sto open)
Click the thunder-like symbol
Select Flashmode and click Ok. (NOT FLASHBOOT MODE!)
Click the (...) in front of the first line of the windows that will pop up
Select the place where you saved file from the above step II on. (This could be a bit tricky if you can't find the place on that Explorer copy/paste the file to the desktop to make it easier. The file won't appear in the window - don't worry it will detect it and load it automatically.)
Make sure everything on the wipe area is checked and that on the exclude area nothing is checked. Misc should be checked too (this is to prevent errors during the downgrade)
Follow the on-screen instructions. It will ask you to press a back button, on the Xperia U it's the VOLUME DOWN button. For some reason you have to unplug the cable from the PC too. After you turn off the mobile plug back in the USB to the PC and then press and hold the VOLUME DOWN key on your phone (keep it pressed and when you plug the USB back in the led's will light up green.) You can stop pressing the button when the process starts on Flashtool's window.
Wait until it's over, you can leave it. It should only take a few seconds
Your mobile will reboot when it's over.
Don't panic if you can't understand what it says
The file your installing is from T-Mobile's HU region. After it starts and you enter your SIM pin, it will take you again through the configuration.
You will have some apps on your mobile from T-Mobile, just uninstall them if you want.
Remember: Flashing will delete everything on your phone so make sure you backup your mobile.
Hope I helped!