Its not particularly encouraging to have this same problem 'fixed' twice, however, that doesn't necessarily mean you were in any actual danger. The oven shorted out, but it should be grounded, so you shouldn't get shocked. However, yes, it does seem scary and its possible (unlikely) the stove isn't grounded.
Are you on a month to month or annual lease? You must have a shitty landlord if you're afraid they'll raise your rent for voicing your concerns over this. At the very least, they should be able to explain why it wasn't fixed properly the first time and what the handyman did to correct it the second time.
As for buying a toaster oven, unless you use the oven a lot, spending $250 sounds like a bit much. Would a $15 thrift store toaster oven suit your needs? We found a pretty nice convection type that we use regularly.