Why does it say "Acharei Achlah"? She did not eat!
Rashi: There no Mapik (dot in the) Hei. It is like Achol [and similarly regarding] Shaso. It [is Makor, like a gerund, which] applies to a male or female. Achlah is a verb, like "Le'achlah" (Bereishis 1:29). Radak - it means after they ate and drank.
Mahari Kara: It means after the time to eat.
Radak: Perhaps after Elkanah coaxed her to eat, she ate a little. 1
If so, why is there no Mapik Hei? Perhaps the dot is missing, to hint that she ate only a little. (PF)
Why does it say "v'Acharei Shaso"? It was discussing Chanah!
Kesuvos 65a: This teaches that we do not apportion wine for women (for it is improper for them to drink). 1
Radak: This Drashah is not precise. (I.e. Radak wrote that Achlah is like Achol; it and Shaso are both gerunds. The verse means after they ate and drank. Radak can agree that the Hei at the end Achlah hints to this Drashah. The Gemara is not precise, for it implies that Achlah means 'she ate.' - PF)
Why is Yoshev written Chaser (without a Vov)?
Radak: It can be red Yashav. Chazal expounded That day he was appointed Shofet. 1
Rashi, Seder Olam 13 and other Midrashim bring this, but they do not learn from the missing Vov. Sechel Tov (on Bereishis 19:1) expounds so about Lot from the missing Vov. Bamidbar Rabah 3:8 counts Eli's 40 years (holds that he was appointed) after Shmuel was weaned.
How could Eli sit in the Mishkan? Only kings from Beis David are permitted!
Radak (from Yerushalmi Pesachim 5:10): Some say that a Kohen Gadol is permitted, but not Malchei Beis David; they learn from our verse. 1
If the Isur is only mid'Rabanan, we can say that Chachamim had not yet forbidden this. 2 (PF)
Radak: "Va'Yavo ha'Melech David va'Yesehev Lifnei Hashem" (2:7:18) means that he settled himself to pray.
Tosfos (Zevachim 16a DH Hagahah) was unsure if it is mid'Oraisa. Mishneh l'Melech (Hilchos Beis ha'Bechirah 7:6) asked, if it is not, why did Kidushin 78b ask how Shmuel was allowed to sit? Perhaps Chachamim did not forbid it yet!
Why does it say "Al Mezuzas"?
Rashi: This is like Etzel Mezuzas.
Radak: It means near the doorpost. This is like "v'Alav Mateh Menasheh" (Bamidbar 2:20), "v'Zavachta Alav" (Shemos 20:21).