My husband recently recently registered as an AE and we have spent the last 6 months understanding who does what.
RSI are responsible for your health cover. If you are a Profession Liberale, you will deal with the offices of RAM who are the part of the RSI dedicated to independent workers. They will issue you with a social security number (if you don't already have one) send you letters asking for proof of identity etc so they can start the process of issuing a Carte Vitale.
A Mutuelle is a company who provide top up health cover insurance. Check what you have been sent from them because you are not obliged to take up their cover. You can choose your own company or even choose not to have Mutuelle insurance. Your Carte Vitale will cover you for 70% of most medical treatment and prescriptions. It's up to you what you do about the other 30% (or more depending on the level of treatment you have, but that is a whole other topic of discussion dealt with much better elsewhere on SFN!)
CIPAV we have been told are the ones responsible for the retirement part of your social cover. As far I can discover, they will send you an attestation telling you you are now in the pension system and thats probably about it until you near retirement.
We make a declaration every 3 months to URSSAF and pay them the cotisations (23,1% of all earnings for a profession liberale). This is the total payment for all the services and URSSAF are just the receiving body.
In addition, you will be required to make a tax declaration (Declaration des Revenus) next year (May) and any tax you may owe will be billed around August 2015.
Beware, you will be sent many letters from organizations claiming you should be signed up with them for health cover or pensions. You do not have to act on any of these unless you want to. They are basically unsolicited advertising.
You may also be sent forms in error so always check what is being asked and if necessary go to your local office and ask.
We have spent many hours traipsing from office to office to find the right people to answer our questions. But what we have found without exception is that everyone is helpful and polite, even if its 'not their counter'. It may take you a little while, but once you have found the right cabinet you can be assured that all will become clear and relatively simple.
Of course, the information I have given is based on my husband's situation as a profession liberale in the AE system. Yours may be a whole different kettle of poissons!
Good luck