Have you been to the Vélib website?

http://en.velib.paris.fr/

I don't use the Vélib since I own my own bike but kerouac (a frequent poster here) uses it and I know other visitors have a good grasp of how the system works so i'm sure they'll come along and answer some of your questions. I can probably answer a few basics.

1) If by another station you mean someplace a few blocks away, that is not necessary. You can check in and check out the same bike but I think you have to wait a few minutes in between.

2) Yes, you can keep it for the day but you better look at the Vélib website to see hourly and daily costs. I you want a bike for a whole day it may be cheaper to rent one from one of the rental stores in town.

3) A helmet is not required.

4) Somebody will probably post a link to a site where you can buy the bicycle map book but they are easily found here in any magazine/newspaper store, bar tabacs and lots of other places. Here are some web sources you can refer to in the meantime:

http://www.parisavelo.net/export.php

http://www.linternaute.com/paris/sortir/dossier/velib-guide-velo/pistes-cyclables.shtml

5) Yes, you can lock the bike as they come with locks.

Since I bike in Paris all the time let me offer a few tips. I would urge you to just go where you want to go on a bike and not spend all kinds of time trying to figure out how to read the bike map book to get to where you want to go. There are bike lanes all over the place and they come in many varieties and chances are you'll keep running into them anyway. Where there are no bike lanes just ride on the shoulder of the road like thousands of other Parisian bikers. Parisian drivers are very tolerant, respectful and aware of the presence of bikers. Your biggest chance of an accident will occur with clueless pedestrians who walk in bike lanes, step off curbs without looking and generally wander aimlessly if they don't hear the noise of a car engine or scooter.

As I said, the bike lanes come in several varieties. There are bike lanes painted on sidewalks, out of traffic (watch out for clueless pedestrians in these). There are bike lanes on the shoulder of the road that are separated from traffic by a curb. There are dedicated bus lanes separated from other traffic by a curb and bikes and taxis are also allowed in these lanes (sometimes bikes are not). There are bike lanes on the shoulder that allow you to go the opposite way on one-way streets and these are just a logo painted on the road with a bike and biker with an arrow pointing in the direction of travel.

If you feel uncomfortable at first then get your map book and start with something easy. Go along the Canal Saint-Martin and further up to the Bassin de la Villette where there are more bike lanes of the type where you are out of traffic. Actually, if you started at the Place de la Bastille and then went north starting on Boulevard Richard Lenoir you'll find these types of bike lanes leading right up to Canal Saint-Martin. It's a nice ride.

Or maybe you could do a bike tour with Fat Tire Bike tours or one of the other companies to get yourself familiarized with biking in Paris.

If you want to keep a bike for a whole day then check the cost of keeping the Vélib all day vs. the cost of renting a bike from a store for the day, which will cost about 15€-20€.

The link provided by FMT above supplies plenty of good information about Velib, and in English. Look sharp at the rates. If you want to pay by the hour (actually half-hour) rather than rent for the day, the rate per segment increases the longer you keep the bike. This is true of other municipal bike schemes too. The intention is to provide commuter transport rather than tourism, so getting the bikes back in the stand for other commuters is encouraged by this steady increase in fees.