Reputation is useless atm.
It used to be relevant when you needed daily quests for fodder t14 to enchant, or in PvP for Bellicarium/KS shops where u needed sometimes certain reputation, but that's long way gone.
Don't even bother checking your reputation tab.
1) I can read online that two daily quests open up when you reach wavering, but I am now neutral and still my daily quest log is empty, is it normal ?
It will stay empty if you're not taking any quest. Those are marked with a green ! and will be placed in your daily quests log once you have talked with the npc.
2) Also, although I keep doing all the quests, I stopped gaining reputation for some reason, I play a level 52 character in a level 39 zone, is it the reason ?
It doesn't matter which level you are, you should be getting reputation as long as you keep doing their corresponding tasks. Same as a level 65 can do level 60 quests around Bastion.
But as Vanquished said, reputation quests are useless unless you're going after the rare black panther mount but that takes a lot of time to get.
Regarding the green exclamation mark, are you refering to the vanguard requests ? I take all the quests that i find and I think I'm talking to all NPCs but the daily quests log remains empty.
Oh I didnt know about that mount but it sounds sweet, thanks 
Regarding the green exclamation mark, are you refering to the vanguard requests ?
That's something closely related (that has green exclamation mark too and gives credits upon completing) but not entirely the same.
You have to manually accept these quests that are marked on the map and above the NPCs' head and they have a set location where you can reach them.
If you accept quests that won't show up in the daily logs then it's most likely just a vanguard quest that won't award you any reputation. They night still give you reputation and credits but that's most likely a one-time, yellow quest.
Ok thank you all 
