If we are going to reduce morality to the way a majority feels about an issue, then in a democratic society, does it make any sense to differentiate between morality and legality?Of course it does, for two reasons: first, there is still a difference between the morality of an individual and of society as a group. Secondly, the fact that society fells something is wrong doesn't mean it has to feel OK with giving the State power to crush it. A good example is Free Speech.
Shouldn't the democratic process eventually result in laws that reflect the morality of the majority?
That would depend on a more pure and direct democracy. But generally they do; when the difference between them becomes too great, people tend to revolt.
But you should remember what I said above: people might feel its wrong to legally punish wrong actions. There's no contradictions in this.
How can you say a law is immoral without taking a vote? For example, if the majority in California voted for Proposition 8, how can it be immoral?
Assuming morality is relative, there's no such thing as an immoral law, because morality is not a property of a thing, but a relationship between a person (or a group of them) and that thing.
So I can say Proposition 8 is immoral, if I find it immoral. Which doesn't mean it's immoral for another person or society in general.
Note: I believe morals are natural laws.
I always found that interesting, because I never found any evidence for that. In what do you base your belief? Or is it pure faith?