So far as I know, it's just the population that matters, and the distance between the initiating planet and destination planet.

So population is relevant to trade?

The Galactic Bazaar has no bearing on trade routes, only on negotiations.

It makes what you offer in trades worth +50%. 

It's a Galactic Achievement and... well it does what GW said it does.  Which is very useful when you're playing the Terrans or some other race with a good Diplomacy, because it allows you to make trades on the negotiating table for a lot less than usual.  Want to buy all your ships instead of building them?  With this GA you really can.

The Galactic Privateer is gone in TotA, because of the exploit it provided. The next best thing is the Korx-only Freighter Command. Both do essentially the same thing, but in a different way: the Privateer makes your freighters invulnerable by preventing any damage from an attack, while the Freighter Command makes your trade routes invulnerable by constantly replacing your lost freighters. However, neither has any effect on the income provided by your trade routes. 

In one game, I had several hundred fleets chasing my invulnerable freighters around the map. It was both hilarious and boring at the same time.

"Mr. President, we got a report that our ships are unable to damage the enemy freighters."

"WHAT!? IMPOSSIBLE! Throw everything we got at those freighters! I want them gone!"

"But sir, that will leave our worlds open for an invasion!"

"I DON'T CARE! Those freighters provide too much of an advantage to our enemy!"

I wonder if a Terror Star would be able to destroy them.   

I wish i never did. I've had more fun with GC2 these past couple of months than i ever did prior. I only regret the community is not as it was whilst i am wallowing in my new found joy.

You are quite right, but at least you found the right way to play galciv2 in the end. Though I never really-really played for score, I did play for "maximum level opponents", which made for some interesting games, but also created a chase after stupid exploits that would give me the edge against the AI. These days I play occasionally, but with some very strict restrictions which prevent me from exploiting "gamey" tactics. Previous game this made for a very fun game as the Yor (who I always avoided in ToA as they are pretty sucky), which was exciting for 14 of the 14 and a half gameyears it lasted.

As for trade (to make this reply relevant to the topic): As has been said, the population of the planets on both ends matters, picking the enemy homeworld as a target is generally pretty good, as it is also a planet that usually won't fall early in AI wars. The distance also matters when it comes to monetary profits, but also consider the relationsbonus a trade route grants you. This is something you should take into account when determining the "maximum profit" you can gain from trade (basically: send a tradeship to every AI you don't want a war with, even if they are very close), they can help avoid costly and unwanted wars and by that method grant you an "invisible profit".

Still, I feel trade is too weak, especially on larger maps, making it hardly cost-effective (even with the relationsbonus). Setting up a range of starbases to enhance it is a very costly way to increase your income a little bit. Trade is also very easely disrupted by war and surrenders, and very fickle in the income it provides (from a pretty nice sum when the trader is far away, to a very small sum when it is close to home).

However, rushing a few trade routes in the early game while playing the Korx can be worthwhile both for an economic boost (making up half of your income for a while, before rapidly falling away) and a diplomatic delay till you can research Xeno Ethics and pick a less offensive alignment (e.g. Neutral). A pet peeve of mine is that Neutral Shipping won't work properly with the Korx as traderoutes are hard capped (at 12 if I recall correctly, or perhaps the research is broken) and the game won't give you all the traderoutes you're entitled to.

Welcome! It is indeed a great game.
 

Whenever a freighter of yours has established a traderoute to another AI, or vice versa, a positive relationsmodifier is activated. You can find these modifiers on the Foreign Stats/Policy screen, under the Report tab. Relation Factors include things like whether your diplomacy is higher (+/++) or lower (-/--) than that of the AI, whether your military is bigger (+/++) /smaller (-/--), and whether there is trade (+/++) or not (neither positive nor negative) between you and that AI. These modifiers change the way the AI feels about you, if it has more positive than negative modifiers towards you, relations may increase, if it has more negative modifiers than positive, relations may decline. Some AI have permanent negative modifiers such as "warmongers" which makes them harder to befriend and more inclined to be involved in wars.

For the trade modifier it doesn't seem to matter whether it was you, or the AI who established a trade route between you, nor does it seem to matter how many freighters there are going back and forth. Any traderoute between the two of you gives you a +, if you are the only civilization the AI trades with, this + changes into ++ (or maybe the ++ is reserved for the most important (= most money) trade partner, but I haven't focussed trade on any AI in ages, so I don't know). In short, establishing a trade route, makes you slightly more likeable to the involved AI, which improves relations or makes them decline less rapidly, making it easier/cheaper to avoid war.
 

It seems you have broken your promise of just two questions! But I will answer anyway:

Your trick is the best may to maximize monetary tradeprofits, though I'd like to add that the earlier you establish a trade route, the more income it will generate. A second advantage is that it is generally easier to defend a single stream of traders, than having your freighters all over the place. It also makes it much cheaper to equip the traderoutes with starbases (though the extra income is pretty shabby, except perhaps on tiny maps). Whether establishing multiple traderoutes is more likely to earn you the ++ rather than the +, I don't know (see above). Trade won't grant you more than two +'s though.

As for the downsides of your strategy: It is very much putting all your eggs in one basket. If for some reason you end up in a war with that single AI, all your tradeincome is completely gone and your starbasemodules become useless. Also if the traderoutes come under attack and you are unable to defend, a single AI fleet can wipe out all your traders without having to cross the entire map to find them. Thirdly, if the destinationplanet or the planet of origin is taken, all the freighters vanish (even if the new owner is not hostile to you). Basically you'd have to establish that that traderoute is very secure, or it becomes a big liability.

The counter to these objections is obvious: if your traderoutes are spread out between many civilizations, the chances of you losing a couple due to unpreventable war are pretty high and defending all of your traders is also much harder when they are spread across such a wide range.

Basically you need to determine whether maxmized trade income is more important or less important than the improvement to diplomatic relations trade gives you. If you want to befriend as much of the galaxy as possible, spread out your traders across different civilizations and just send one to each capital (well defended, good population, and a civ that loses it capital will no longer require +trading in relations as their military is most likely very weak) until you've reached everyone. If you want to make as much money possible on your traders, send them as far away as possible, to a high population planet, and then defend this traderoute and the AI you're trading with.