Hello. Well I'm partly going on my own experiences and partly what I think works in the game. I actually don't have the legalese language available to me at the moment and so I don't claim that my interpretation is correct per the RAW.

In my game:

-Healing Endurance damage while in Travel mode does not occur.
I do not interpret being on the road as a safe comfortable place. I have already given my in-game reasons for it; I will also say the following. I was in the Marine Corps for 8 years and we did from time to time as you'd expect of infantry, "hump" or hike, usually 12 to 25 miles in a day or a day + night. Trust me when I tell you there is nothing therapeutic about these experiences nor does your body "heal" in the space of a single night. Generally, in fact, your body is more likely to continue to break down the longer you do it. You get rashes and chaffing where your gear cuts in. Cramped muscles are only made worse in the morning. And blisters? Oh the blisters. I've seen tough men cry over blisters on the foot. Now whether you consider these circumstances as "Fatigue Gain" or "Endurance Loss" I suppose is up to you. And how serious you consider Endurance loss to be separate from an "Injury" is also up to you. A sprained ankle, a bruised rib, an infection or open sore...trust me when I tell you these things are not prone to healing while you are hiking upwards of 20 miles a day with 50 - 100 lbs of gear as an adventurer in TOR would be required to do. That's partly my interpretation.

There are exceptions to my ruling, however. If a player scores particularly well on an Explore check I might allow them to find accomodations that are well suited for the night; the right combination of food, water, good air, and a clean, comfortable, warm cave could work.

-Weary Condition Going Away on the Road.
I'm ok with the Weary condition going away on the road, as long as the accompanying Endurance gain occurs to trigger that. I see no need to double-punish my players since I already make Endurance gain difficult.

-Resetting Travel Fatigue:
I haven't really decided this one, but generally speaking, I'm not ok with it just occuring on the fly. Again, I think back to my time in the Marines and also doing the Greek Indpendence Day in NYC marching 3 miles in Hoplite Gear http://www.thegreekwarriors.com/joinourgroup.html, 5th guy down. I can tell you from experience that it takes sometimes a whole weekend, a hot bath, and a swedish massage from a lovely woman to get the kinks out of the muscles.