My Ninja isn't 90 yet but I believe most, if not all, of your questions have similar answers regardless of which Melee-oriented is asking. These answers are just my opinion so take them how you will:
1. Cap your primary weapon merits first (i.e. Katana) followed by Evasion. After those I would say it's all down to preference in regards to which order you level the rest in, especially with Ninja-specific merits. HP and Strength would be my final 2 things to upgrade once I'd capped everything else I wanted. If I were to choose I would put HP as dead last in the merit order due to the pathetic amount of HP you get for spending that many merits.
2. Quests/NMs are the most efficient way of getting your seals. NMs in particular would be the fastest route to obtaining your AF3+1 upgrades. NIN, with the appropriate sub, can solo a fair few of the seals needed and the rest wouldn't be hard to shout for in Port Jeuno. Just research the seal you need, the NM that drops it, other notable drops and then shout in Jeuno for people to help you. State that the seals you need are locked and that the rest of the items are free for the other members. If you don't know how NMs work in Abyssea you should research the Weakness Targeting page of FFXIclopedia.
3. For Ninja you would ideally want Sky and Sea since the best earrings for TP come from both of these. Brutal earring and Suppanomimi are what you would be ultimately aiming for. The Suppanomimi is gained from the Divine Might quest which can be used to complete the Ark Angels missions in the Rise of the Zilart expansion. This quest is actually unlocked AFTER you get access to Sky, which is why I say Sky is something you'll want to aim for since you'll need to get it anyway to get the best earring. Also, from completing CoP you gain the Raja's Ring which is one of the best TP rings in the game. Dynamis is also handy but a lot of the gear from there has become more and more situational as newer gear outshines it.
4. Advice for Abyssea? It is often better to low-man NMs than take an alliance along with you. Alliances feed the thing you're fighting unnecessary TP and if the mob has dangerous TP moves it can be more trouble that it's worth. Also the more people feeding TP, the more TP moves are used and the harder it is to proc a weakness.
Another tip for exp parties; have a movie or something on in the background. Abyssea gets monotonous pretty **** quickly when you're on your 3rd/4th job to 90.
I'm a pretty cruddy player by all accounts so you should wait for more responses before acting upon mine since Ninja is not my main job and has barely any merits in it yet. Good luck!
Edit: Just in case - proc means to trigger a weakness on an Abyssean NM. Here's the FFXIclopedia
page on Weakness Targeting that I stated above. Edited, Aug 20th 2011 5:31pm by Diamondis