Tax question - Inheritance from UK living in USA

I am not a lawyer (IANAL) but the US (Federal) government exempts the first half million (+/- $250k). That's why you don't owe the Feds.

States can tax you separately. (+counties, +cities/towns/etc.)
The percentage you are taxed on might be after an exemption (I see an exemption on the first $40k).

Check with a tax CPA in Nebraska, you may have options since it is from out of the country (like not realizing it until you convert it to dollars, or until you bring it to the US).

Also, for what it is worth, I don't see your 18% figure anywhere.
I see a 1% rate in NE for a child after your $40k exemption.
Ref: nolo.com/.../nebraska inheritance tax

Yes, you need to file a 3520 if the amount bequeathed to you was over $100k USD, however it should not incur a (federal) tax burden.

You will not need to submit an FBAR unless you have foreign accounts over the threshold. So if you have more then $10K USD in your UK account(s), then yes, file the FBAR. Note that the FBAR requirement has nothing to do with the inheritance per se, it's required only if you have a foreign account open with more than $10k in it.

Nebraska has specific limits for inheritance taxes. If your father was not a Nebraska resident when he passed, then I believe you are not taxed on the inheritance. I'd like to see another comment or answer to support this part of my answer. Supporting info:

The Nebraska inheritance tax applies to persons who die while residents of the state or, regardless of state of residence, who die owning real property located in Nebraska. [ ... ] The inheritance tax is administered by the county court of the county in which the decedent resided or in which his or her real property is located.