Backup with/without TimeMachine

Hello Mac'ers,
of which I am a newbie, bought my first mac 4 days ago and of course am loving it, and apologise for my ignorance.
However..... in my struggles setting up my 2 mail accounts I accidentally deleted the contents of the 1 that was actually working and lost all my emails, and I cant seem to recover them.
I realised maybe I have to setup this TimeMachine, but it seems to want an external harddrive only, I havent partitioned my internal harddrive so I cant backup to that.
Questions: 1 Is there somewhere I can restore what I lost?
2. Am I right about needing the external to set up TimeMachine or can it be done without formatting my internal and loosing everything (the little I have managed to accumulate in the 4 days) on it.
Looking forward to hearing from anyone who know more than me
Cheers,
Dorthe

Welcome to the Forum. Partitioning the Computer HD defeats the purpose of backing up - Consider if u back up using TM to 2nd partition and the Drive fails you have nothing. The likelihood of 2 HDs failing at the same time is much more remote, so splash out and get an Ext HD. It will pay off in the long run.
Meantime check McBies comments here then decide which system is best for you.

Will do, Thanks much.

And sorry, your e-mail account is probably lost No worries after you set up time machine though, its a big relief just knowing its there...