Asalamu 'alaykum....(1) Is it sufficient to wipe the head from front to back only (not from back to front again) while doing wudu? (2) Is there any problem to wash the feet with the both hands simultaneously while doing wudu?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.

It is sufficient in Wudhoo’ to wipe over the head from the front to the back once without wiping again from back to front. Wiping the head again from back to front is a recommended act of Sunnah as underlined in Fatwa 92419, but the important thing is that the whole head must be wiped.

Al-Kaafi reads, “However the head is wiped is sufficient, with one hand or with both hands; however, it is recommended to pass one's hands from the front to the back of the head, then bring them back to the front of the head where he started.”

Ibn Qudaamah wrote, “If one has hair that he fears might be ruffled if he passes his hands back over his head, then he may refrain from passing them back. (Imaam) Ahmad stated this. It was said to him: "How should one who has hair down to his shoulders wipe (his head) in Wudhoo’?" He wiped his head (from front to back) once and said: "Like this, to avoid ruffling the hair," i.e., he should pass his hands to the back of his head and does not need to bring them forward again where he started (to the front of his head)."” [Al-Mughni]

There is no harm in washing the feet with both hands. The important thing is to make sure the water properly reaches the whole body part being washed.

Allaah Knows best.