Yes, you can use the IFL in IAD as well as the Arrivals lounge in FRA. Just show your BP. It is a pity that FRA-HYD is two class, otherwise you would get the lovely FCT at FRA. None the less, there Senator lounge is the best of your options. You might be allowed into one of the regular First Class Lounges if you show your BP from IAD-FRA, but I doubt it.

Not sure about DEL, but the SEN lounges typically have showers in FRA. You can use the RCC as well, but I think you go on a lower priority because you are not arriving on UA. The SEN lounges usually have better showers.

Isn't DEL-FRA 3 class? If you're in F you are entitled to use the FCT in FRA I think. You definitely are if your FRA-IAD is on LH. Either way, you can still use the IFL in IAD.