Why does it say they bowed in front of Hashem?
Malbim citing Chazal 1 : He needed to take leave of Hashem again.
Malbim: They went to bow because their Tefilah was accepted.
Tanchuma Bereishis 13 learns so regarding departing from one's Rebbi, from Melachim 1 8:66.
Why does it say that he was intimate with her after they returned home?
Rashi (from Kesuvos 65a): This teaches that intimacy is forbidden 1 for a guest [at an inn].
Even according to the Drashah that she became Nidah when leaving Shilo (refer to 1:18:2:2), and even if Elkanah lived within a week's journey, and she could not become Tehorah beforehand, since the verse mentions intimacy after returning home, we may infer this law. Really, it is an Asmachta. Nevi'im do not teach Halachos! (PF)
