Many of them were purged, yes. Strong alien species (like the Saiyans) were used as warrior races (and given much more freedom), usually destroyed for one of four reasons: Frieza had reason to believe they were too strong, they were rebellious, their leader(s) were against Frieza, or Frieza was in a bad mood.

Often, a few of a species who were already part of the army or fled were spared. If these events happened.

On your first question, Frieza had himself, Zarbon, Dodoria, the Ginyu Force, and many other strong members of the army with incentives to keep it in check, most often monetary rewards and vast freedoms. You must remember, many species would be killed if they did not support Frieza, and promptly could have been conscripted into the army. Also, Frieza owned the majority of the galaxy - hundreds of planets and therefore hundreds of species to join his army.

Hope this helps!

Frieza and his father King Cold operated on fear. They were mutants with great power at their personal disposal and could even destroy entire planets on a whim. They used these powers to form a very profitable business known as the Planet Trade Organization. While Frieza and Cold were more than capable of wiping out entire civilizations themselves they were not warriors at heart and didn't much care for the tedious work of clearing out planets and thus employed a very large corps of workers to do so. The Saiyans are but a single race in a very large organization that doesn't just include warriors to take these planets. In fact historical archives show that the Planet Trade Org employed many scientists, engineers, technicians, doctors and administrators to keep the whole thing running.

To answer your question regarding how races came to join the Planet Trade Organization we can find evidence again in the historical record specifically in regards to unnamed members of Cui's race. During the ill-fated Namek campaign, soldiers were watching the battle unfold on another planet with a large scale scouter. One soldier cursed Frieza's name and wished his defeat for destroying his race. Another member of the same race executed him for treason on the spot while remarking that Frieza's actions had raised his family's standing. Given his uniform we can take it that he held a high rank in the Planet Trade Org.

So what does this mean on practical terms? The Planet Trade Org is always looking for new talent to fill its ever growing ranks. As the company expands its operations the demand for an ever larger employee body become greater and greater. This is especially true for races and individuals that show exceptional combat prowess. Given that officer's comments we can infer that when the Planet Trade Org came to conquer his planet his family ingratiated the forces sent somehow and secured themselves a good position post conquer.