1) Do you have anything(s) of significant value if the home you are renting goes up in flames? If so, most likely, those things won't be insured unless you get renter's insurance. The landlord's insurance probably won't cover loss to YOUR belongings unless something happened that you can prove gross negligence on landlords behalf.
Example: you left a candle in a room and the entire room catches fire. Your personal belongings are insured by your renter's insurance, not the landlord.
2)Liability coverage. Suppose you have a guest over and something happens and the guest turns around and sues. Whether the liability is you or the landlord is a grey area:
in some cases it's the landlord (roof shingle falls off and injures someone walking by)., in some cases it's you (you stack a bunch of heavy boxes in the garage and it falls over on a guest walking into your garage). Part of renter's insurance have a liability coverage, if you don't already have any.
How much for renter's insurance depends on coverage. Not an insurance agent, and not a renter. So no idea. But it's easy to call around. AAA,allstate,farmers,etc.