Corrected entry: The star collapsing into a black hole suddenly seems to increase its gravitational pull on the planet that SG-10 is on. When an object collapses to a Singularity, the pull it exerts on an object does not suddenly change because the mass, and therefore the strength of its gravity, has not changed.
Correction: Black holes certainly increase gravitational pull and can tear planets apart. In additions, black holes are pulling in matter around it, adding to its mass.
A star and a black hole formed from it have the same mass and cause the same gravitational pull on objects outside the star's original diameter. Yes, a black hole pulls in matter around it, but that is the exact same matter that would also be pulled into a star of the same mass, so again the star and black hole would have the exact same effect on everything around it, including the planet. Regarding black holes (and stars) pulling planets apart, that is from tidal forces that grow exponentially as they approach a large mass, and again for objects at a distance outside the stars original diameter a star and black hole of the same mass cause exactly the same effect. The reality is when a star collapses into a black hole, some of the matter gets ejected and causes a supernova during the process, so the planet would have been torn apart long before any black hole was present, with the planet's debris thrown away from the event, not sucked towards it.
No, the gravity on surrounding objects does NOT increase, unless the black hole absorbs sufficient amounts of matter to increase it's gravity noticeable. Merely turning a star into a black hole won't affect objects such as orbiting planets.
Correction: The gravitational pull of the Singularity doesn't change. The SG team simply didn't know it was there, and its effect increased as the planet's rotation caused the black hole to "rise" in the sky. Just as the Sun doesn't get hotter or colder during the day, it still feels hotter at midday than at sunrise.
Your analogy is flawed because the sun's heat is blocked by the earth until it has a line-of-sight, while gravity's effect goes through the planet. A black hole millions of miles away would have no noticeable gravitational difference during the different phases of the planet's rotation - noon or midnight. The only way what you said would make any sense is if the black hole is small and close to the planet, but then that wouldn't be a black hole from the planet's star collapsing since the mass and distance would be wrong.