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Did you try to turn on glove mode and try if sensitivity of the screen changes?
About problems with restarting, there is a way to turn off the phone when it freezes.
See this post Xperia SP frozen
Wi-Fi problem is not so easy to solve, for better solution we'll have to wait for people at Sony to solve it.
But one thing I did try, and that was to change my Wi-Fi settings. Was searching for better signal reception, and found that i got better reception when changing default Wi-Fi channel on my router and setting network mode from mixed 802.11b/g to just 802.11g.
For some reason, no one of my neighbours didn't change their "most popular" default values of their Wi-Fi channels so most of traffic in my building is on the same network frequency on channels 6 and 11. So I've changed my Wi-Fi to channel 1 (which is in +/-5 channel range, meaning less interference), and gain some "free air". For now is holding quite well, much less problems with network disconnection.
Maybe you can find some "free air" in your Wi-Fi space.
If you wan't to try; I was using android app Wifi Analyzer on my XSP and inSSIDer app on my laptop.
Would strongly recommend to not to buy this phone. I am using this phone for past 8 months and have little to tell you abou it. It fares pretty average in battery life and has a buggy code. Now my speaker is not working.
Don't buy this phone. The bugs can render some of the basic functionalities annoyingly useless. Wifi and walkman glitch in particular. Worse, the software updates are constantly adding new bugs. Sony really took for granted a great hardware.
Regarding the restart - if you lift the back cover off, there is a tiny hold in the back with the word "OFF" written by it - if you put a pen in there, it restarts it. There is also an option in the settings somewhere that restricts the phone from connecting to a WiFi network if the signal is weak. It might be that box is selected.
I would not recommend this phone purely because the Bluetooth handsfree volume during call is so very low and it is unusable. Many people have had the same problem and we do not seem to be getting any help from Sony.
There are lots of other issues reported on this forum but I not had any of those myself.
If you want a phone with usable Bluetooth handsfree and support from the manufacturer then this is not the phone to get. It is a real shame as I think it is a nice looking phone.