I can understand where your coming from, it would be hard to keep that vein of loneliness and guilt going throughout a long series like this without it getting annoying or stale. But I think they are actually handling it (At least the on paper version of it) fairly well in NewWho, Eccleston fresh from the war is dark, brooding, riddled with guilt. Tennant is starting to get over it, dealing with it, dealing with the fall out of it, trying to come to terms with it. By the time we get to Smith he just wants to forget about it and move on, so he becomes more childlike, more interested in getting out and seeing the universe again, but he can't escape it, he keeps coming back to him, and when it does it hits him hard (The Doctors Wife for example, he wants so hard to just accept that the timelords are dead and gone so that he can move on, but when even the faintest glimmer of thier exsistence emerges he is suddenly thrust into it again, and when it turns out it's fake, it's just like another gut punch all over again).

As far as having another Timelord to bounce off of, I like the theory but I don't think another Time Lord is the answer. A) It completely nullifies the ENTIRE idea of him being the last time lord there will ever be, think about it, there is only one Doctor (And unless there's some major factor of TimeLord biology I don't know about they don't procreate asexually) and he is the last there ever will be. But put another in the mix (And I think I'm right in this, but Time Lords don't technically have genders, they can regen as men or women, so they could technically reproduce...I'm way off the reservation thinking on this one, if there's something in the canon I don't know, feel free to correct me) so if there are 2, technically they could adam and eve the entire time lord race again.
B) I've always viewed the Doctor Who universe in the same sort of light as I look at the Hitchhikers Guide universe, the universe is endless, and there is all sorts of shit out there you don't even know about, so much no one could ever see it all. And yet, on the show we only ever see a very small fraction of it (Both literally, any amount of infinite possibilities is a small amount, and figuratively: What we do see is always so surface level, there is very little actual depth to most of what we see. Run here, save these people, run here, oh that's cool, save these people, run over here etc etc. My thinking is, is it really so ridiculous to think that there is literally no one else in the ENTIRE Galaxy with whom the doctor could develop that kind of connection?! Seriously?

We got a little hint of something like that with The face of Bo, but it was so brief if you blinked you missed it. But out there in the universe there has to be someone with whom the Doctor could talk on something nearing an even level, even if the other person doesn't EXACTLY understand whats happening that doesn't mean it won't be useful. I mean imagine if an ex-Time Agent was suddenly cursed with everlasting life and walked the universe for a few millennia as a lost soul doing some pretty fucked up shit that he has to live with...I imagine he and the Doc could have a pretty solid convo... not that I've thought explicitly about that at any point *cough* Er...right... moving on...

But idk, I kinda get frustrated sometimes when there's ANOTHER Dalek episode or Cybermen, I mean there is this boundless, endless universe out there that we could be exploring and we can't get away from these damn guys (Which yeah, I get that's the point in universe, but as a viewer of the show it gets frustrating sometimes) It's actually why one of my favorite sequences from New Who is the scene where Smith is going around calling in favors and rounding up troops for the assault on Demon's Run to get Amy back. It made it feel like the Doctor actually has this entire life outside his Companions that we never get to see, and actually has friends out there in the universe. And I love that stuff.

Sorry, long, rambley... probably makes no sense... apologies.

I think it's part miscasting, but her character is also written horribly. The weird time tripping shit they tried to pull around her makes absolutely no sense when you step back and look at it, and as the seasons went on, it felt like they were just trying to jam and force in more and more twists, without actually bothering to justify any of it, or make any of it make any goddamned sense.

I like River when she's just being that coy, playful, kickass warrior thief chick who knows just a bit to much about the Doctor. But it's when they try cramming all this extra shit into her character that the entire thing just falls apart.

And yes, I think another actress would be much better suited to the role.