Could we detect an alien starship entering Earth's Solar System? Or in it?

I think we could detect #1 fairly easily if we happened to be looking in that direction. Given the amount of time it would take for that sort of “drive” to slow a massive interstellar ship, we’d probably be looking in the right direction at least once.

#2 might be detectable if the Bussard collection scoop was visible in itself or caused a visible effect. Most Bussard ramjet designs use a large magnetic scoop to magnetically accelerate hydrogen from a volume several kilometers in radius in towards a small fuel intake, and this might cause the hydrogen to emit light of some wavelength, which someone who’s taken more chemistry than I have could tell you.

Of course, if the ramscoop itself has mass and a relatively high albedo, it might be large enough to be visible. Then again, if we’re talking about a massive net with a high albedo surrounding a ship, we’re basically talking about a solar sail, which would probably be visible if aimed directly at us and might or might not otherwise.

Radio telescope applications for Types #2 & #3?