- Should I spread all those religions or should I only spread the state religion?
Not necessarily. Every one you spread will give you +1 gold (if you have built the holy shrine) and +1 culture in your own cities. So I would spread them in all of your own cites. However, for enemy cities, you might only want to spread one religion. For maximum diplomatic benefit, you may want all neighbors to be a single religion (that you then match). If you spread Hinduism and Judaism to your neighbors, as an example, one might convert to Judaism and the other to Hinduism, which could create problems.
- Does it cause unhappiness in the city if there are multiple religions?
No. In fact, it improves happiness if you build multiple temples. Plus, if you switch to free relgon later, happiness is boosted even more. There is zero downside to spreading multiple religons withn your own cities.
- How do I change the state religion?
F7 and then select the religion you want.
- And how do I built the Shrine that get others to pay tribute?
You need great prophets. Which means you need great prophet people points. Some wonders will give these (Stonehenge, for example). You can also manually generate these points with priest specialistis. Once you get the great prophet, move them to the city that founded the religon (will have a star on the religion symbol) and select the holy shrine option.