How long would the Earth last if the sun became a black hole?

[Quizatzhaderac]

if a very small black hole did fall directly towards the sun from interstellar space, would it actually stop? Concepts like friction don't really apply to black holes. I guess the singularity would get more inflowing momentum from its direction of travel, so it would slow down somewhat...)

If it's small enough and fast enough it wouldn't stop. It's even been theorized that the Earth has been hit by several black holes.

That would change the orbit, wherever the Earth is would become the new apoapsis, the periapsis would be significantly closer, possibly within the roche limit

If I calculated it correctly, Earth would not be in the Roche limit. Although Venus and Mercury would enter it.

The Earth-Sun Roche limit is only about 110% of the sun's radius (the sun is not dense). If we octuple the Sun's mass¹, we double the Roche limit. Assuming the new periapsis is no less than an 8th of an AU, that still leaves a fair distance.

¹ The Roche limit equations from wikipedia use the sun's radius and density, but those exactly cancel out if you keep the mass constant.

Edited for math mistake