1) How do you know it's love?
...Read this maybe?
If you feel differently with them than others, like happier or more flustered I guess? I don't really know o-o
2) How do you get the person to know that you love him/her?
Tell them in some way (Best and hardest would be to tell them face to face. Don't rely on others to tell them since they might not take it seriously o-o)
3) If the person follows another religion, is it a problem?
Depends on the religion. Some are strict with love, but if you find yourself really loving them then you might change, which will be a way to show your love too, I guess. But if something screws up then uh..
If their parents objected, the best course of action... To me would be persistence o_o; Find why their parents object, and do your best to prove yourself or make it better.
I'm not the most religious person in the world so I wouldn't really know.