It seems you can self certificate it all if you are capable.
No you self certify full stop.
This is in the UK and EU, in the USA things are very different.
You need some evidence as to why you said it was CE complaint. An offense is only committed once your product has been tested in a certified test house and found not to comply. You will then be "visited" and depending on the due diligence you showed / not showed, you will either be helped to comply or they will throw the book at you, or anything in between. Penlites range from a fine to equipment confiscation.http://www.electronicsweekly.com/blogs/test-and-measurement/2010/07/is-uk-really-sharpening-its-teeth-for-ce-marking-enforcement.html
In the U.S. I believe the fine is per product sold so if you sell 100 then you get the fine (I think $2,000) times 100.
FCC has two categories:-
1) Intentional emitter (RF energy) - this needs an FCC number which consists of two parts. One unique to your company, and the other unique to that product. This is for things like transmitters including RFID readers and some types of tokens. This certification is difficult and expensive to get and you need to interact with FCC or an FCC agent to get it.
2) Unintentional emitters - that covers everything else electronic. You do not have to contact FCC but you have to have the appropriate certificate produced by an FCC authorised test house to back up the FCC logo on your product. If you do not have the logo marked the equipment may be confiscated at import. The galling thing is that every minor change requires a new certificate, so if you have 10 products that are all very similar unless the only difference is in the labeling you need to put each one through the test house. So if the LED is a different colour, it needs it's own test certificate. In my opinion is is actually a form of import control.