As far as I know, you can't rollover an inherited traditional IRA to an inherited Roth IRA.
If you withdraw the funds from the inherited IRA and pay the taxes, then the remaining money in your bank account is just money, and you can do anything with it that you can do with other money. That includes contributing to a Roth IRA, following all the normal rules about contributions ($7000 per year, must have compensation from working, etc.). If the inherited IRA is larger than $7000, I do not know of any way to rollover the entire amount to a Roth IRA, even if you are willing to pay the taxes.
As far as I know, you can't rollover an inherited traditional IRA to an inherited Roth IRA.
If you withdraw the funds from the inherited IRA and pay the taxes, then the remaining money in your bank account is just money, and you can do anything with it that you can do with other money. That includes contributing to a Roth IRA, following all the normal rules about contributions ($7000 per year, must have compensation from working, etc.). If the inherited IRA is larger than $7000, I do not know of any way to rollover the entire amount to a Roth IRA, even if you are willing to pay the taxes.