All right, there's a fair bit to unpack here.
Taking this one-by-one...
Damn...they really don't like me
That's definitely true of at least two of them (the Jurinn and Kaan-Visam), yes. It also appears your relations with the Vissari are nearing a tipping point, although possibly not beyond repair just yet.
Your relations with the other three (Bryll, Hissma, & Triech), however, aren't actually horrible. No, they're not great, obviously, but if your relations are higher than -50, then the situation is definitely still salvagable with them (though maybe not easy).
It will take some effort, however, including a bit of...generosity on your part. Giving gifts (energy credits, minerals, favors, etc.) are a necessary part of making friends in Stellaris. In addition, it's generally best to start giving gifts as soon you make contact with someone (if you can afford it), before relations have a chance to begin degrading. While that's obviously not possible with the folks you've already met, it's good to keep in mind for the future.
Also - how come my fleet is limited to 24 (was 20 but I had extra for research) because of pop but the "enemy" factions are far superior with a similar pop?
Setting aside the possibility of AI cheating (I suspect there might be a bit of that going on), naval capacity is mainly determined by a combination of numerous factors: civics, technologies, traditions, certain job types, etc. In this case, all it would really take would be for the other nations to have researched the first technology that increases naval cap (which is entirely possible -- it usually shows up in the first several decades); that alone would probably be enough.
My universe - all mine muuuuaaahahahaha
Then again....
Looking at the first screenshot, I notice a number of things (that could make a sizeable difference):
1,) At the moment, you're a fair ways behind the others in expanding your territory. You need more star systems -- both for the resources, and for new planets to colonize.
2.) To do this, you of course need alloys (for building Outposts), which you currently have very little of. However, you have plenty of minerals and food. Sell some of them (one or a bit of both) on the Galactic Market so that you can purchase more alloys...and then send your constructor ships a-building!
3.) When you have vessels that are idle (such are your 2 fleets and the 1 construction ship) and don't plan to use them in the immediate/very near future, dock them at the nearest Starbase with a Crew Quarters module. This will cut down their maintenance costs and save you a little bit on energy credits.
4.) I see your science ships (and their Scientists) are sitting around idle. They should always be busy, especially in the early game! Keep them surveying systems, researching anomalies, etc. I would also recommend building a third science ship (once you've purchased more alloys), as that's going to help a lot with getting those systems surveyed more quickly.
5.) You have a lot of influence just sitting there, unused. Hopefully you'll be able to start quickly spending some of that for building Outposts in new systems, but it might worth checking (if you haven't already) to see if there's any available Edicts that might be useful in helping you get things kickstarted/caught back up. (If there's one that improves alloy production or research, that would be especially nice.)
