1)
Why did he tell her "Lechi l'Shalom"?
1.
Malbim (from Brachos 31b): This shows that one who incorrectly suspected someone must appease him.
2.
Radak: This was a prophecy. This Shalom is from me, but your Shalom is from your Creator.
2)
Did Eli pray for her, or inform her that her Tefilah was accepted?
1.
Rashi: He informed her that her Tefilah was accepted. Radak - since the Navi informed her, she felt good and ate.
2.
Radak: Perhaps he prayed for her.
3)
Why does it say "Shelasecha"? It should say Shelasecha, with an Aleph!
