"mongoose traveller how many career terms can you take": Well, this is an easy one. By rules as written, there is no hard limit. The two primary limiting factors on safe careers like citizen, noble, and merchant are aging and the advancement roll rule. Aging is much less of a threat for profitable / rich classes, since they can afford anagathics. However, page 9 of the Mongoose Core states:
If your result [on an advancement roll] is equal to or less than the number of terms you have spent in this career, then you cannot continue in this career after this term. Either your services are no longer required, or events have caused you to leave, or perhaps you are simply bored and want a new challenge.Thus, no character can do more than, oh... 15 terms (assuming they roll all 12s to advance and end up with a 15 in their advancement stat) in any one career, even if they make all of their survival rolls. Granted, most characters will also be decrepit with age or lousy with anagathic debt by that point.
In practice, however, even 6-term characters are terrifyingly skilled, equipped, and well-connected. General consensus on the Mongoose Traveller forums is that limiting PCs to a maximum of 4ish terms produces heroic, but not ridiculous, characters. As a player in a 4-term-limit game presently, and having GMed a 6-term-limit game last spring, I can attest to this statement.
"powergaming mongoose traveller": And now we start to get into the funnies. Look, kid, I don't know who sent you here, or why you think I'd know anything about powergaming. Oh, that post. Look, that was back in d20; I'm a reformed character now, I am... ah, crud... Fine, come in, and have some theorycraft, but you didn't get it from me. At first, it seems hard to powergame in MongTrav because the character generation is so damn random compared to d20. However, there are a couple things you can do to help your odds. First, roll high for ability scores (just kidding... high scores do help a lot, though). If at all possible, go for a Vacuum / Asteroid homeworld; Zero-G and Vacc Suit are both important to have, and you don't usually need more than 0, so background's great for those. Finally, cultivate a good understanding of probability theory; it's your best friend during Trav chargen (well, besides your dice).
There are a couple 'standout' careers which tend to be strong in play and chargen. Marines are scary dudes in combat, especially if you can roll Armour for combat armor. Ideally you want to be rank 4 - this gives you a 1/3 chance of rolling armour in each material benefits roll, as well as two extra rolls. If you get to rank 5, then your odds go down to 1/6 per benefit roll; the fact that you gain one extra roll is unlikely to offset this reduction in probability. Agents have a fearsomely good entry on their Events table (number 8, so it occurs just under 1 in 6 events) where they go undercover, and if they pass Deception, they can get a Rogue skill and a roll on the Rogue events table, which includes a goodly number of events which give another skill. So if your dice like rolling 8s, Agent is a good choice for raw skill generation.
Navy's Personal Development table is good, since there are no skills one it; there is a school of thought that says you should try to accumulate no skills during character generation, just ability scores. Then, when you start play, you can rapidly train up exactly the skills you want. I've never seen this done in practice, but if Mordecai dies, I may have to try it. Going Navy for 4 terms and ideally getting promoted each term, you'd end up with 8 skill rolls, which would give you about +1.33 to each ability score by expectation. If you don't get Commission (and per page 8, "trying for commission is optional."), then you'll end up with Mechanic 1, Vacc Suit 1, and +1 End from ranking up. Looking at the Navy events table, your expected Skills Per Event yield is around... 1 in 3, plus a small variable factor based on your Edu bonus from Event 5. Thus, expect about 1.33 skills from events over 4 terms. When you muster out, you're at +9 points of ability scores and ~3.33 skill rank. If you refuse Connections and Skill Package skills, then you can learn a new skill in about a month, which is insanely fast in Traveller terms. You'll suck pretty hard at the beginning of play, though, and you can accomplish a superior skill flexibility for mental skills with a Wafer Jack for much cheaper (more on those later), so be sure to focus your training on those physical skills you can't learn from the Jack (like Gun Combat, Zero-G, and Vacc Suit. Those are the Big Three physical skills that everyone should have. Stealth and Pilot also get honorable mentions. In the mental category, you cannot go wrong with Recon, Medic, and Mechanic).
One trick I stumbled across with my current character was a result of the 4-term limit. I finished my third term as a Thief at rank 3 and realized that if I changed careers, then got promoted, I would get an extra benefit roll and any skills gotten at rank 1 on the new career's promotion table. Basically, odd-numbered ranks are good, generally - Thief 3 / Merchant 1 got me 7 total benefit rolls (4 from terms, 2 from rank 3, 1 from rank 1) and Broker 1, whereas Thief 4 would have gotten me 6 rolls and no Broker.
If you roll Athletics, Coordination is great because it lets you throw grenades and knives, as well as climb things. Endurance, however, may actually be better, but is less obvious; it lets you resist stunners, poison, and disease, as well as wake up from unconsciousness more quickly. Stunners are really, really good, so being able to resist them is also very nice. Strength is the weakest (har har) of the three (well, except for Flight for non-avians...).
So those're the set of hacks I've discovered so far for CharGen... there are also gear selection things, but those are much more straightforward. Do buy Reflec; lasers kill people. Especially buy Reflec if you're wearing Combat Armor, since you're a big fat priority-one laser target otherwise, and Reflec stacked on Combat Armor makes you scarily durable. Wafer Jacks are great, since you can load up on cheap Expert/1 chips of mental skills and then use them at 0, or gain a +1 DM on checks below a certain difficulty if you already have the skill. Paid for itself about 100 times over just for the +1 to Broker. Stunners are excellent against lightly armored targets, slug autoweapons are good against light-to-medium armored targets, and lasers are your best bet against heavily armored targets. RAM Launchers are terrifying. There is no reason not to carry a snub or body pistol and a dagger, since they are weightless. If your weapon has any recoil at all, install a gyroscope even if you don't think you'll need it, because you may take Strength damage. Always, always get the laser sights. I think that's about it... Upon further consideration, this could've been its own post. Oh yeah - also, if you can get your Broker DM up to +3 or +4, you can make enough money to buy Miami. This is left as an exercise for the reader.
"klingon ship color schemes": OK, this one I actually don't know anything about. I hereby refer you to the honorable Sergeant Crunch.
"character dossier assignment": Oh, you poor bastard. You're here because of that "Character Dossier: Asmir the Faceless" post, but you're actually looking for something homework related. This amuses me.
"accordion thief nemesis quest": Well, there's something I hadn't thought about in a while. Haven't played KoL in... not really sure. Beginning of last semester; September, maybe. So that's like six months. However: the accordion thief nemesis quest is the worst of the six nemesis quests. I commend you, brave soul, to the tender mercies of the KoLwiki page on the subject.