1. Billions.
2. Little to Nothing. Because they wouldn't make it as far as fast as the Voyager probes because they got a massive gravitational assist from a rare alignment that only happens every 176 years. All the other planets needed to be aligned appropriately for this journey at this speed. New horizons may leave the solar system in 43 if we don't lose contact. And they already want to shut the program down. NH is about 10000 km/h slower than Voyager 1.

Best to use targeted probes to explore things we haven't before. Ask different questions and if they leave the solar system, good on them. But I'd prefer orbital data satellites around all the ocean moons in the outer solar system.

Maybe I could have been more explicit. Without the planetary alignment that made the voyager probes possible an equivalent mission would be ridiculously expensive/impossible due to the fuel requirements (and wouldn't be able to visit all of the planets)

If starship/new glen/the rocket lab one work, it might become more feasible.

Instead, sending smaller, simpler probes that just visit one planet/moon would be much more cost effective, but still expensive.

We have already got a lot of the low hanging planetary science fruit from existing missions. New missions would need new/novel sensors or need Landers/aircraft which make them much more expensive.

Even just a 'standard' interplanetary mission isn't just an out of the box job like current earth satalites are becoming.