Did the Soviet Union ever send people to the moon?

No.  While the Soviets did have a manned Moon Landing Program underway in the late 1960s they just couldn't get their N1 heavy launch vehicle to work.  It had a perfect launch record - it failed four times out of four launch attempts. 

The fourth launch attempt failed only two weeks before the US launched the Apollo 17, the final lunar landing mission of the Apollo Program and the Soviets decided to cancel the N1 rocket.      

No but they sent a  monkey

No. The Soviet crewed lunar programs were a series of programs pursued by the Soviet Union to land humans on the Moon, in competition with the United States Apollo program to achieve the same goal set publicly by President John F. Kennedy on 25 May 1961. The Soviet government publicly denied participating in such a competition, but secretly pursued two programs in the 1960s: crewed lunar flyby missions using Soyuz 7K-L1 (Zond) spacecraft launched with the Proton-K rocket, and a crewed lunar landing using Soyuz 7K-LOK and LK spacecraft launched with the N1 rocket. Following the dual American successes of the first crewed lunar orbit on 24-25 December 1968 (Apollo 8) and the first Moon landing on July 20, 1969 (Apollo 11), and a series of catastrophic N1 failures, both Soviet programs were eventually brought to an end.

Yes. Yes, they did. They established their first moonbase on August 12th, 1968 and it has, by now, expanded to cover the far side of the moon. Hope this helped.

No.  They tried, and they even designed and I think built their equivalent to a lunar module, but they didn't get there.

They had a program to compete with the U.S. (actually two parallel competing programs) but they weren't successful.  One of the biggest causes of their lack of success was repeated catastrophic failures of their chosen heavy lift launch vehicle.

One of which created so much devastation that it took a year and a half to rebuild the launch facility.  And produced enough damage that U.S. satellite photos proved they were (secretly) working on a manned moon program.

Incidentally - that failure took place less than two weeks before the launch date of Apollo 11.  The first successful manned moon landing mission.

No.  The Soviets, along with the Chinese, and I believe the Indians, have sent unmanned probes to the moon.  But the only people to walk on the moon have been Americans.

No. They put the first man space but did not set foot on the moon, although they landed a probe or two. The Americans landed about twelve men on the moon before scrapping the Apollo missions.