I just found Safari to be a bit slow and it kept locking up forcing a restart of the phone
?? Don't think I've ever seen it lock up the phone and I browse on my phone a lot. You mean completely frozen so the Home button doesn't work??
You know you can kill background apps by double-tapping the Home button, then long press to start them wiggling and red circle to kill them. You should be able to kill Safari like that if you really have to.
Definitely no need to reboot the phone.
Also the slider on youtube seemed to be not very responsive
Also odd. You mean the scrubber bar at the top presumably? One thing that isn't immediately obvious is if you press on the bar then drag your finger down then you get finer control (on the bar is Hi-Speed Scrub, down a a bit is Half Speed, further down Quarter Speed, then Fine Control).
the touch screen itself doesn't seem as responsive as my old phone
?? And again odd. I can touch mine lighter than I can feel and it responds. You did take the cellophane wrapper off yeah??
It could well be that your phone is a bit borked, though it is hard to know without seeing it.