could be "я хочу зараз літо"
Yep. But when "зараз' is in the end it puts more emphasis on it: "I want summer NOW", which is what people usually want to say, when they are saying something like this :)
When do you use 'тепер?' Or is this an older word?
Тепер - lately, nowadays, recently
Зараз - at this moment/second, at the time of speaking