the sun - Could our Sun be a companion star of a massive black hole?

There is no indication nor any astrophysical reason for such a scenario. The most relevant constraints are

1. The Solar velocity is typical for stars in our immediate Galactic neighbourhood.


2. Soft binaries (those with orbital velocity smaller than the local velocity dispersion $sigma$) dissolve (Heggie's law: soft binaries become softer and hard binaries harder).

These are in contradiction with a Solar binary nature: a viable binary has a large orbital velocity that would put the Sun outside of the typical velocity for local stars. This contradiction can only be temporarily avoided if the current (but not in $sim1000$ years) orbital velocity and the velocity of the massive binary companion add up to a typical stellar velocity. This is an unlikely chance.

Binaries with a stellar-mass black hole always form from an ordinary stellar binary, with one of the stars going supernova. Often, such binaries are quite compact. All this is ruled out for the Sun.

Finally, black holes of intermediate masses (100 to $10^5$ M$_odot$) haven't (yet?) been detected unambigously (though there are several objects that have been claimed to be such intermediate-mass black holes also IMBHs).