How many colonies can be put into a sector

Go to contacts - empires and select your own empire.

Hovering over the icon containing a building and two flags (either under diplomatic status on the left or in the list) tells you about all your embassies.

Additionally under diplomatic status you'll see the flags of all the empires you have embassies with and can contact one of them to recall the embassy by clicking on it.

I've found no upper limit to the number of entries in my situation log, research or otherwise. I also have no reason to think that there will be a limit.

Furthermore, I've found that you can research many of these simultaneously.

At the start of each game, you will encounter several alien life forms that will produce research entries in your situation log. These all pause the current society technology. According to @Kexlox, the research points during this time are not actually spent on the alien life form research, but are instead saved to be doled out later in a slow release.

So, you wouldn't lose any research points, but you might get your technology a few months later than you would have otherwise, depending on how close it was to completion.

But, I've noticed that, for some reason, you can research all these life form projects simultaneously. So, waiting until you have a handful all ready and doing them at the same time can minimize the disruption to your research, as compared to doing each one as it pops up. I've researched at least six at the same time before.

I would not be at all surprised if that turns out to be a bug, and is fixed in a patch at some point.

Update:

I've been playing after the Unity DLC, and the bug mentioned above appears to have been fixed. There's still no limit to the number of entries in the situation log, and you can start several of them at once, but it seems that only one progresses at a time (per research type).