My Iphone gets hot and the battery runs out really fast?

Now I have an Iphone 4, and I've never had any problems with it but since a couple of days the screen gets really hot if I use it and some apps don't work properly. If I want to check my mail then it will open and it closes itself. Also the battery runs out very fast, the other day I charged it till 100% and I left it unused for an hour of two and when I checked it when I wanted to use it, it was on 30%.Is there something wrong with my battery? Do I have to get it replaced?
Thanks!

Added (1). I haven't dropped it in water or on the ground recently.

Well your using the iphone 4 which got out 2 years ago, just wait for one more month because in september the iPhone 5s is being released and i'm sure everyone will love it! Itll have the fingerprint lock feature, iOs 7(which is amazing) and more apps and i bet ull love it if your an apple fan. Your phone is old, just buy a new one plus i bet ull even like the LG G2 and the note 3(releasing this september too) CHHEERS!

So what it seems like is your phone is burning way more energy than it should.

Some things that might be affecting the energy usage is… Your case (if you have one). Your case most likely keeps the heat that the Iphone produces thus making the Iphone hotter and it isn't good for electricity so your phone gets hotter and uses more electricity.

Another thing it could be the apps you actually haven't closed. If you press the home button twice it shows all of your apps that are secretly open. To close them for good, hold on app for about 2 second and they will all shake and then an X will appear on each and you can close them.

Finally it could be the electricity. It is good to not have the phone charging all of the time, doing this basically makes the phone more dependent on being constantly charged, when you unplug it, it just "forgets" how to save battery. It's like its addicted to being charged and then its withdrawal. So try to not have your phone plugged in a lot, only for getting the battery back up then unplug it even if you aren't using it or going to.

Those are three things that usually effect that sort of stuff. You could also get a battery saving app. I have one on my phone and my phone goes for days without needing to be charged (of course not being used every minute)

So yea, I hope I helped. As for your mail closing, try closing it like I said earlier and try again. If not try restarting your phone (turning it off then back on). Still nothing then I guess google the problem or contact apple

I don't know why your apps are malfunctioning but here are some was to make your battery last longer.

Delete your runnin apps (double tap home button, hold down an app, then tap red x)

Turn location services off

Keep in mind that using apps uses more battery then other functions such as listening to music
Hope this helps