Question

Why was the Russian Civil War fought?
The Red Terror in the Russian Civil War was viewed as the only way to eliminate political opponents.
The Bolsheviks were worried that Tsar Nicholas Il would come back into power at a future date.
The coalition that formed the White Army did not want to see the Bolsheviks create a communist state in Russia.
Foreign countries wanted to make sure that the Red Army did not make Russia a communist state.

Answer 1

Short answer: It was fought because the Bolshevik seizure of power in October 1917 split Russia into many hostile camps with competing political goals, and those tensions exploded into a multi-sided civil war fueled by social breakdown, national movements, class conflict, and foreign intervention.

Now a quick check of each statement you gave:

1) "The Red Terror in the Russian Civil War was viewed as the only way to eliminate political opponents." — Partly true/nuanced.
The Red Terror (from 1918) was adopted by the Bolshevik government and the Cheka as a policy of mass repression to crush counter‑revolution and intimidate opponents. Bolshevik leaders considered harsh measures necessary to survive a violent civil war and internal plots, but it wasn’t literally the only view in Russia — it was their chosen and systematic method.

2) "The Bolsheviks were worried that Tsar Nicholas II would come back into power at a future date." — Misleading/inaccurate.
Many anti‑Bolshevik forces were monarchists who wanted restoration of the monarchy, but Nicholas II abdicated in 1917 and the imperial family was executed in 1918. The Bolsheviks feared a monarchist or other anti‑Bolshevik restoration more generally, not specifically Nicholas II returning to power.

3) "The coalition that formed the White Army did not want to see the Bolsheviks create a communist state in Russia." — True.
The White forces were a loose coalition (monarchists, conservatives, liberals, former imperial officers, nationalists) united mainly by opposition to the Bolsheviks and their program; preventing Bolshevik rule was a central aim, though Whites disagreed among themselves about what should replace Bolshevism.

4) "Foreign countries wanted to make sure that the Red Army did not make Russia a communist state." — Largely true (with caveats).
Allied powers (Britain, France, Japan, U.S., others) intervened for mixed reasons: reopen an eastern front against Germany early on, protect war supplies, support anti‑Bolshevik forces, and counter the spread of Bolshevik revolution. Ideological opposition to communism was one important motive, but strategic and material concerns also mattered.

Brief synthesis: The civil war was therefore driven by the Bolshevik revolution and the refusal of many groups inside Russia (and some foreign governments) to accept Bolshevik rule, plus social and economic collapse, regional and national separatism, and catastrophic wartime conditions.