1. Not really sure what you write about (could be reasoned by my lower skill of english language). Do you talk about techs or improvements ? Can you upload a screenshot, perhaps ?

2. The bonus is for your home system.

3. You can show/hide the pings for attack or defense requests for your allies by the small icon attached to the lower left of end turn button. If you left mouse click this button, you can choose to set these pings on your own (2 new icons appear/are displayed above). You can even write additional text within a box attached to the ping you place on a system. All (human) allies can read this.

4. Outposts get lost

a) in case another players fleet sieges it (activated by shield symbol) and attacks supporting logistic fleet(s)  preventing them to build up the outpost or 

b) if another players outpost is finished sooner than yours threshold 

If you zoom into the system you did found an outpost, there are icons below the outpost, that you can activate to trigger an action (i.e. send food, drain food from enemy outpost in same system) for to lower the turn duration until your outpost is finished and colony is founded. To the left side you can change the system, from where you get support ships (food, i.e.) to speed up the process. What options you can choose of to speed up transform outpost to colony process, depends on chosen faction. I.e. The Unfallen do vine systems and can insta-colonize.

It's one of the galaxy-wide unique buildings. The player who finishs this kind of building first, is the only one having it. 

Other players that tried to build it (but didn't succeed in time) get some dust to compensate the amount of invested industry.

You first have to unlock these buildings by progress in research tree.

In case another player conquers a planet containing a unique building like that, he/she should have it's bonus instead of the previous owner.

There are other unique buildings, what any player can build one time only within his/her empire. They are marked similiar like the galaxy-wide ones in building queue.