So I am new to game and am enjoying figuring things out and doing my first playthrough.  

I wanted to mare sure I kinda understand this.

If you build an infrastructure improvement that say adds +x food to river tile, 

You would not gain that food on a river tike that you've built on, if you've built something other than a farmers quarter?

But yoi do gain them from what would be indirect exploitation?  

So a maker's quarter that exploits a river in neighboring hex would add the extra food for you? 

You'd then lose this food if you built a quarter on this hex that wasn't a farmers quarter?

Is this correct? 

Also a harbor improvement (fishery I think) adds +3 food to harbor.  Does that add it to only the specific Harbor or all the hex that the harbor exploits?

From what I understand:

+2  food on rivers counts river tiles where a farmers quarter has been built upon, along with the Harrapa farmers quarter that counts as a river. So the tile itself still gains the +2 food, as the farmers quarter still exploits it.

Both River infrastructures combine into a total of +4 food generation on rivers, and that tile above the canal network is generating +5 from exploitation and +1 from Feudalism. 

All yield bonuses to tiles apply only to exploitation. To get food bonus, or any food at all, on a river tile you have to exploit it with an adjacent farmer's quarter. To get both food and industry from a tile you need an adjacent farmer's quarter and an adjacent maker's quarter while leaving the tile empty. This is why exploiting rivers is usually awkward.

I've notices this as I've paid closer attention.  

I still feel like harbors are weak. I'm sure someone or many have mentioned, but not letting then act as a "hamlet" is at best poorly conceptualize and at worst, idiotic. 

Either 

A) Have harbor food upgrades apply to all except exploited tiles

B) Let me build something attached to a harbor. 

Also, it's ridiculous that I can buy a Harbor for like 100 Influence as an outpost but it takes forever! To actually build one.  

Yeah I never understood why I could buy things with influence on an outpost, but not on a city.

Evolena wrote:
2.) But the one that adds industry to forests -> the bonus (and only the bonus) counts even if the industry of the forest tile is not exploited (ie the tile is exploited, but not for its industry).

It must have to do with how each one is worded, but it's not very intuitive.

I learned something again. This is a real wtf moment for me, yet again. I mean it really doesn't matter, since forests will most often have their industry exploited anyways (its the only thing they produce) but how can a bonus industry be applied to a tile that doesn't get its industry exploited?