Is the prayer valid if the intention for prayer was not made immediately before the opening takbir, and is the initial intention for both Dhuhr and Asr prayers sufficient when combining them, even if I did not call to mind the intention for Asr before performing it?

The doubt of a questioner regarding prayers he has already performed is not to be heeded, and doubt after completing an act of worship is not considered. As for the intention to combine two prayers for someone who combines them at the time of the first prayer, many scholars have made it obligatory at the beginning of the first prayer. It is more prudent to intend the combination when commencing the first prayer for one who combines prayers with an early combination (jama' taqdim). A person afflicted with obsessive whispering (waswasah) is advised to adopt the easiest of opinions.