IPhone 4 :: Malware Opening Tabs In Safari And App Store Applications

My phone was given to me by someone else but I did a complete reset and deleted their data and started using the phone.Everything was fine until I went on to a few questionable websites. Having clicked a few links, I found that new tabs were spontaneously opening in the safari browser and the app store kept kicking me out of my web session and inviting me to install some app.Â

As far as I am knowledgable, the phone is not jailbroken (if it was this would have been rectified when I did the reset, correct?).And as far as I know, the phone is very much safe, as long as it is not jailbroken, from malware etc. I did yet another reset, several intact, and I had a similar issue. This time though when I did the latest reset I did not include my iCloud and apple id credentials during the set up for fear of getting hacked. Â

The problem now is I have the issue on the phone, there is a lot of data, numbers and pictures I would like to transfer to my computer but I am 1) fearful of connecting it and 2) afraid to type in an email and password to send my data to myself, or even sync everything with iCloud.Â

The phone is also terribly slow, I don't know if this is a malware problem or if it is, as I read others have said the same online, the phone being too underpowered to support iOS 7.Â

Info:
iPhone 4, iOS 7.1.2