No, any taxes would be paid by the decedant's estate before distribution is made of the inheritance. Exceptions are funds received from certain types of trusts.
Generally, no. The estate pays the taxes with the exception of traditional IRA's and retirement plans if you are the beneficiary (not the estate), then you would need to pay the taxes.
If you inherit money that has never been taxed, such as a traditional IRA, you will pay income tax. If you inherit money that was not subject to income tax for the decedent, you will not pay income tax.