WanderingKid

Yes, it will, because you are very close to the same orbit, but not exactly on the same one.  There is no way, really, to be 'exactly' on the same orbit in KSP.  You can get incredibly close if you can get directly behind (or ahead) of the object on its orbit and you're killing relative speed directly on the prograde/retrograde orbit markers as well, but in reality it's almost impossible to do.  I say almost, because someone is going to come in here and show that it *can be done*!  For the rest of us mortals, however...
You can kill relative velocity being four kilometers away from the target, or even on the other side of the planet (though prepare for a mess that way).  All relative 0.0 means is "For now, at this VERY moment, our vector velocity matches".  That's not orbital velocity, that's vector velocity.  So if you think of two ships, one on a lower orbit and one on a slightly higher one, and you're directly underneath the higher one (from the planet's view) and match vector velocity, your orbits will cross up ahead and behind.  Eventually, you create an X from that vector matching, because you're starting from a different orbital position.  That eventual X creates a different vector velocity difference.
This is why typically, when docking, you do three or four burns to get yourself much more aligned with the target orbit.  The first one is a gross change, to get to a reasonable difference and then closer to the target... and its orbit.  The next few are adjustments where if you had a NASA team behind you telling you exactly what marks to hit you wouldn't need, but we approximate by simply burning at the target then correcting a few times by killing relative again at closest point.  Finally, your last docking approaches and adjustments match your orbits to near exactness.  Note, I say near.  If you don't dock you will always find you've had some drift after a while when you come back.

I'm not sure about OPT Space Plane Parts, but I know the COL/COM indicators can lie even with some stock bits.  If it's not registering lift off the pieces in the front of the plane, your COL is WAY up front.
I'd start with dragging those forward swept wings WAY back and seeing what happens.

My guess is you didn't center the kickbacks onto the staging component.    So, they're probably actually attached to the liquid tanks directly.
One of the things I've found is you have to make sure where you've grabbed the SRB (where your mouse is) you need to make sure it's on top of the decoupler.  The way to really make sure it's attached is once you've hooked the SRB on, grab the decoupler, and if they both come off at once, you're hooked up right and you just need to make sure the staging is straight.  If you only get a decoupler on your mouse key, you're not hooked on right.
So, check your model in the hangar, and then if you're still having trouble, can you post a screenshot with your staging?

For some reason RCS tanks seems to be very weak for holding onto heavy things.  If your design was flipped over, where the light part was on the outside, you'd be in a better position.
I know a few possible ways to deal with it, but I wouldn't call any of them great.
One is to strut the orange tanks to the RCS tanks.  That will help with the snap off they're incurring.
Also, accelerate at say 1/5 to 1/4 the burn rate until those orange tanks are empty and the mass is less.  Annoying, but the lack of g-force should help keep them attached.  You will probably want to experiment to find out where your limit is.

What antenna do you have on the probe you're hoping to talk to the probe with the HG-5, and what level have you upgraded the tracking station to (that's mostly curiosity)?
Short form: The range is not 5million meters from the HG-5, it's a combination of two antennas.  Your Hermes satellite is at 2.7m range.  The average combination of an HG-5 relay and a Comm-16 antenna is ~1.5m.  Your antenna is way too high.  You want 3 of them ~500-600km up in my experience for the early comm net.