Sometimes I wish Apple would just delete these threads after they have run their course because I think they do more harm than good. So much hypothesizing from a couple of well intentioned (hopefully) users.
I know it's been a while SuperNMY and you probably have this all straightened out so I am posting this in case someone else comes along who may be having similar issues.
I have seen this very same behavior on my phone. However instead of assuming there was a virus I drew on past experiences to feel at ease about the situation and take corrective action and I am sure that my hunch was correct.
My phone got full and in the background Apple downloaded the IOS update which resulted in even less space available. Like desktop computers there is temp space or swap space used in the course of normal opperation. If the flash drive or the drive on your computer gets too full you can see really strange behaviors. I have seen this many times.
You might even hit several buttons without realzing that each command you were initiating would attempt to run once the phone could catch up but couldn't due to too small of an area to write the commands it had finished using back to disk or to memory (if any was available). So they all ran in sequence making your phone look like it was possessed. With regard to the email getting sent. I have questions for you on that. Do you have a password set on the login screen and if you do, are you POSITIVE no one has ever seen you enter it? That's the most likely explanation. Someone mischieviously sent an email either from your computer or your phone.
So the key question to ask is: "How much storage space is available?" This needs to be one of the first questions you look at during trouble-shooting an issue.
Here is what I did...
1. Went to Settings/Usage/ and checked Storage available. I had 32GB which was nearly full. You will note the spinning circle that indicates it's doing something. Let it finish and it will give you a report on space used by application and how much space each application is using. It will list the applications consuming the most space first. I noted on my device that the first app was a game my daughter was playing and it was unusually large. The first thing I did was to delete that game. After which I closed all apps and power cycled the phone. Response was much better when the phone came back up and I found I could navigate more easily so I went back and started deleting all the stuff that I wasn't using or that was taking up too much space. This included downloading photos and deleting them from the device. (Which is how I roll normally).
2. Look for Apps that use storage space that may not be obvious. Most of them will allow you to move/delete/copy from the Itunes application when you are connected to your Mac. If that's not possible then mail things like recording, PDFs, Photos, etc to an email account or offload them using Phone To Mac or some similar app. There are several and some will even let you do it before you buy the Desktop Application.
Once I had cleaned the phone off of all the unused items I power cycled it again. When the phone came up again it was running great. Commands were executing quickly again. I had to do this same process once more when the IOS 7 update came out because I didn't have enough space to download it. My hunch is that this is what your problem is. You also don't indicate which model of phone you have. If you are trying to run IOS 7 on an iPhone 4, it may not really run well.
That's my .02 cents.