a. can the USco claim back this VAT if it is charged? - No, unfortunately not. VAT taxes are not considered an income tax which would generally give rise to a tax credit. The USco will only be able to claim this as an expense.(IRC 162)
b. is the USco obliged to pay the retrospective VAT and can it be enforced? - I believe that the VAT must be charged by the UKco providing the service. The UKco is responsible to hand over the tax to the HMRC. Whether or not the UKco actually collects the VAT tax from the USco is irrelevant. The UKco will be expected to remit the VAT tax to the HMRC.
c. Can the USco charge US sales tax on the resale value of the goods back to the UKco? - quite possibly yes. Depending on what state USco is domiciled sales taxes may actually be required. (such as Washington or Florida)
My question is whether USco can claim this tax back through the US tax system OR can charge US sales tax on the sale to the UKco - The USco cannot claim this tax as a foreign tax credit as the VAT is not an income tax. The only thing the USco can do is expense it as a IRC 162 deduction. As mentioned above if the USco is domiciled in a state that requires sales taxes then yes it should be charging sales taxes to it's foreign customers.
I trust this provides the clarity you were looking for, please let me know if you have any further questions.