Hey HPSH, I had almost thr same issue with my Xperia Z3 but instead of my browser opening, different Apps I had installed were opening or my messaging would open and start typing words like, xywqk wuz... I I uninstall thr Apps and it still did this, even in Safe Mode. This was with AVG antiviral installed and my last option was a software repair, which worked. I would recommend a software repair as well but would also put the phone in Safe Mode first just in case that might be the problem so you don't have to backup everything. (Sorry about the length by the way.)