The Spanish used the mission system to settle and protect its long and exposed frontier. The territory north of Mexico City was referred to as the Northern Frontier.
The driving purpose (from the king’s perspective) was to protect and hold territory Spain had “discovered” and claimed. Missions were the fastest and most economical way to settle this vast territory. It simply was not practical or affordable to send large numbers of soldiers and settlers. Missions were not unique to California. With some local modifications the Spanish used the mission system in Texas, Arizona, New Mexico and in many parts of Latin America to settle their “frontier.”
From the church’s perspective (and for individual missionaries) the most important objective of the mission was to convert the natives. A pair of padres was assigned to each mission; one who focused on spiritual affairs and the other managed temporal matters. In reality recruiting neophytes, and building and operating what became a self contained large community of with hundres of inhabitants took the majority of the time and effort of the padres. Some missionaries, perhaps the majority, would have preferred to function as simple priests.
However, the missionaries knew that in order to survive in the wilderness and receive the continued support of the crown, the missions had to become viable communities. When financial support from Spain began to diminish starting about 1810, the missions were under great pressure to produce more food and goods (cured cattle hides and tallow) that they could trade these for necessary supplies and manufactured goods, so the emphasis shifted even more to the operational aspects of the mission. By this time, too, the established missions were far flung enterprises with one or two mills, vineyards, farms and ranches spread over as much as 40-50 miles.
So you are right, the purpose of the missions was both political and spiritual. However Spain was a Kingdom and the decision to settle California was made by the King and funded by the state. The church would have preferred to see this happen much earlier than it did.
As to your last question, the mission by definition was not just a church but a community and no mission could have survived or functioned without the Native Americans. They did all the work, from constructing and repairing buildings to planting the fields and tending the herds to (in the case of the women) making clothing, cooking and washing.
Theoretically the Native Americans were converted and joined the mission voluntarily and this appears to be true, particularly in the early years. One doubts though, whether the Native Americans had much of a grasp of what daily life would be like. The California Indians lived off the land and it must have been a shock to move into a highly regimented, agricultural society where one was expected to work a good deal of the day. From what I have read some of the Native Americans, particularly those born in the missions, came to prefer this way of life. Others tried to escape. Run-a-ways were a big problem (10-15% of the population).
Leadership was also a factor here. The most successful missions had inspired padres who really cared about the neophytes and created a climate where the majority wanted to stay. Fr. Peyri at San Luis Rey was such a man, and when he finally left the mission to return to Spain he had to escape at night because the neophytes tried to prevent him from going and when they discovered he was gone scores of them rode to San Diego to try to prevent his ship from sailing and get him to change his mind.
If you are interested in this topic you might want to read Indians, Franciscans, and Spanish Colonization: The Impact of the Mission System on California Indians by Robert H. Jackson and Edward Castillo.