I This the techs you are refering to are the terraforming techs. Some planet tiles are initially unusable, but once you research those techs you can build the improvements that let you use the tiles. Example you have a planet of PQ 11, and it has 2 yellow tiles you can't use yet. Then you research soil enrichment. Then you build soil enrichment on those two tiles. Once those are build the PQ of the planet will be 13. Then you can use the tiles normaly. the same goes for the other two techs down the line...habitat improvement and terraforming. They just work on different squares. So that PQ 11 planet might be PQ 13 after you research and build the soil enrichments, PQ 14 after you build habitat improvement and PQ 17 after you build the terraforming. It's just radom how many of each you get per planet.

Also you probably haven't noticed beceause the games default setting is auto-build these improments once you have researched the techs. So your planets have probly been building them and you just haven't noticed.

You're not noticing a difference because it's a percentage increase.  So any planets that are under class 20 won't benefit from a +5 PQ bonus and any planets under class 13 won't benefit from a +8 PQ bonus.  At least, that's how I remember it working.

And as far as the planets you haven't colonized yet-the bonus is only applied when you come into possession of them.

There was an issue in DL & DA where the PQ bonus didn't work properly in some fashion (I don't remember the specifics, but I believe it was working on planets you colonized, but not those you invaded), however it was resolved for TA, somewhere in between 1.95 and 2.0.