1. Do trade and trade good have anything to do with each other?

Yes, in the sense that trade goods can be traded much like techs, money, ships, etc.

2. Or are trade goods just the same as any other super project.

Trade goods are essentially tradeable super projects. Meaning they provide civilization-wide bonuses like super projects, but unlike super projects you can trade those bonuses to other civilizations.

3. Do they increase the income from trade routes? If so, does this apply for imports or exports or both?

Trade goods do not inherently improve trade route income. (I don't know off-hand if there is a trade good that provides trade bonuses.) You need to build Economy Starbases, research Trade-related techs, or build certain Planetary Improvements for that.

Trade goods are called such because they are goods you can trade, not because they necessarily affect trade routes. I think the confusion is the semantics of Trade Routes Trade vs. Diplomacy Trade. Trade goods are a Diplomacy Trade sort of thing.

Think of it as say, your civilization has patented a formula for an Aphrodisiac, for example, and thus is manufacturing the stuff for your citizens with all the benefits thereof. If you want you can give/sell/barter a copy of the formula to another civilization so they can also produce the stuff, but you can still continue produce the stuff yourself as well.

4. Does this only apply at the planets involved or is it empire wide?

Empire wide.

5. If you give another civilization the goods via diplomacy, do they then gain the same bonuses? Do they have to build the good first?

If you sell/barter/gift a trade good to another civilization it does gain the bonuses from that good (you still keep your own bonuses, as well). It does not need to build the good first. It cannot trade that good itself to others, you retain exclusive trading/selling rights.

6. Do you then get less money from trade routes with them?

No.

Peace & Luv, Liz

Oh. That's a shame. I thought it would be kinda cool if you could work trade goods into you economic strategy to increase the value of trade routes. Like +1bc per export route if the home planet had a trade good. I like being able to develop an economic strategy like that.

Another question. Can you build a freighter at one planet, then use it to start a trade route that begins at another one of your planets?