Are there any plans to build a telescope the size of our solar system?

No, there are no plans.

Why? Because it's actually a very difficult thing to do, forgetting about the cost for a second. You're basically asking about interferometry, which works because we can sync up the dishes to roughly the same size scale as the wavelength we're interested in. For radio waves, this usually means around 21 cm or so. So, we can build an interferometer if we can align the dishes to more accurately than 21 cm. That's not too hard if the dishes are next to each other. Now, consider your Plutonian case. Suppose one dish is on pluto and the other on the sun (of course you wouldn't put it there, but humor me). The fastest we can communicate with the dishes is the speed of light, which means it takes around 5.5 hours to communicate between one dish and the other. Again, you won't put them there, you'll put them out at Plutonian distances, so that's roughly 11 hours apart (again, you might stagger them around and decrease this time a bit). So, now you have to align the dishes to better than 20 cm, but it takes ~10 hr to communicate between them.

Let's picture it: You tell one dish to ask the other dish, "where are you pointed." Wait 22 hr. It says, "I'm pointed over here. Where are you pointed." (22 hr because you have to send the signal there, then it has to send one back) Then you say, "no, you should point slightly over here. Wait 22 hr. Uh oh, now the telescopes have moved a few centimeters, now you re-align. Wait 22 hr. ....

You get the picture? Interferometry is very hard. It looks easy on Earth because of the proximity of the equipment. Nowadays things like the VLA are a rousing success, but new versions (like LoFAR) are struggling to get started. Connecting dishes across the solar system is a gargantuan engineering problem, money be damned.

We could barely scrape together the funding for the New Horizons probe to Pluto, it's hard to imagine that anyone has such grandiose pipe dreams for observatories at that distance. Hell, I'll be happy if we can even get the Webb telescope into space, and it is mostly already paid for.

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We might someday find it possible to deploy some sort of distributed orbital radiotelescope 1 AU out (that is, roughly as far from the Sun as Earth is), but as far as I know there isn't anyone currently holding any kind of realistic hopes of such an extravagant project. It's just a guess on my part, but anything like this is probably a century away at best.

No plans, unfortunately, but if we could set up an interferometer array about that size(for which we'd only need 2, rather than six individual telescopes, assuming we could coordinate them sufficiently well; of course more would be better, but there's the law of diminishing returns to worry about with funding) it would be awesome. We could probably get reasonable resolution of things like exoplanets. If a serious proposal for something like that comes in, I'll happily chip in my portion of the cost.

That's the unfunny truth about science funding. Nearly everybody thinks its a good idea except for the Congressmen that vote on it. They would rather see money go to defense contractors that promise to build in their home districts or just stuff dollars into their re-election war-chests.

Is there any wonder why Congress has a 7% approval rating?

No, we are not. You say the size of out solar system? Well most of our solar system's mass (99.89%) is in the Sun, meaning that we would need to use more than the Sun's mass to create one bigger than the Sun. Also, you really do not grasp how big the Solar System really is and how empty it is. The Solar System is mostly empty so we literally would not have the necessary materials in our closest 100 star systems to make one that size,

Not at present. We've not yet reached the limits of what we can do with the Earth as our baseline for interferometry. I think once we have a few scopes on the Moon we'll start thinking about interferometry on an Earth-Moon baseline.

By the time we were capable of building something that big we wouldn't need to; so no there are no such plans and never will be.

No financially impossible