1) Is there a software (free or not) that could help me to speed up my work?
There is PLENTY of excellent freeware around for subtitling.
However the hidden cost of subtitling is skimpy guidance, no tech support, in other words, you must know what you are doing.
Also, it's not a matter of speeding up your work, but making it possible for you to accomplish some level of quality.
Quite frankly, this depends more on you than the software you use.
2)We only have to make a translation or we need to know how to add the subtitles onto the movie?
This depends on the kind of clients you cater to.
Producers and subtitling studios will want translation work only.
Clients whose core business does not include/involve video will require the whole nine yards, they'll want a finished subtitled video.
3)What's the rates for English to Spanish translation?
Shake a beehive, count how many bees come out of it, and each one will have a different answer to this question.
My advice is, first learn to do it! Second, check how good is your output, compared to what's in the marketplace. Then check how much people charge to do a job about as good as yours.
4)The clients provides us an original subtitle to work on or do we have to start from scratch?
Honestly? Anything may happen. There is no rule for this.