A. Why does Tolkien identify Ithilien’s climate with the Sea? What does it mean that to Gondor, the Sea is South, not West?

Moist winds mean warm rains.  The Mountains of Shadow catch the rains (thus Mordor is dryer) and the water that falls on them is relatively untainted -- note that Sam isn't properly in Mordor and unable to wear the Ring till he crests the pass.  The Morgul pass is a gash of evil through the neutral mountains.

B. Does Tolkien use such sleep imagery anywhere else?

In the Withywindle valley, perhaps?

C. What time of year is the right one?

Summer.

...A good day for strolling
D. What does this remind you of?

The Green Hill country in the Shire.  Roads go ever on, but not without lunch, etc.

E. Should such a change [from Feb. to Mar.] have affected the seasonality of this chapter, with its flowering plants and warming airs, and stronger sun?

It was probably too nice for February.

F. To the degree that Tolkien wrote his story to work with the seasons, isn’t this Ithilien sequence a bit of a ‘false spring’? Or am I going too far?

Lothlorien was similarly springlike.  Not false so much as temporary.  Something to work for?  Like life vs. heaven?

G. Would anyone care to work out how this information [about Lent] does, or does not, apply to Tolkien’s story?

Forty days before the destruction of the Ring (Tom Shippey has noted that March 25th was traditionally thought of as the first Easter) would be February 15, which the Encyclopedia of Arda tells me was the last full day in Lothlorien, and the day that Frodo looked in the Mirror of Galadriel.  The day they got serious again, if you will.  Shortness of food is a subject in this chapter, and there'll be fasting in Mordor, for which Tolkien in letters identified religious significance.  I have no idea what day was Friday.