How and when do you recover hope points?

You recover Hope by spending Fellowship Points or Protecting your Fellowship Focus. The later comes in two parts - if your Fellowship Focus is unhurt at the end of the session or if you spend Hope to protect Fellowship Focus, you recover 1 Hope. You can also take the Virtue Confidence too.

You start each session with Fellowship Points equal to the number of members in the Fellowship plus an extra one for each Hobbit. This is a refresh, so it doesn't accumulate i.e. spend unused Fellowship Points at the end of a session. There are some additional bonuses IIRC like Twice Baked Honey Cakes.

Is there any way to recover more Hope during the Fellowship Phase?

This came up a while back, though I forget the thread. From the sounds of it, the consensus was that Fellowship Foci and the Fellowship Points were the only ways to recover Hope, and that Fellowship Phases should not allow it. However, I personally feel that if the Fellowship Pool refills every session, that time frame would fit into a Fellowship Phase, so a lengthier Phase would justify a refill of Hope, but I am aware that I seem to be in the minority in thinking this.

No. You could give Hope as an award for a particularly spectacular event (this is hinted in the book) but it would be a very rare occasion.

If you run a long session, common sense says you should award more Fellowship points.

I've been running single-player sessions for a little while now and have had to work around to Fellowship Pool for Hope recovery. Not wanting to bind the Hope Recovery mechanism to any need to maintain a "fellowship of NPCs", I took a cue from the quote on page 28 of the LMB where the characters feel invigorated by the presence of an awakening tree spirit. I wouldn't use these "Inspiration Tests" too often in a group setting, but if you find Hope too hard to come by in your present circumstances, please consider the following:

https://www.dropbox.com/s/m9whbbfoi5v07to/T...%20Recovery.pdf

Cheers,
Dankers