CE compilance on radio modules for
1) No idea

2) There are two sets of CE radio tests: the generic immunity/unintentional emissions tests required for all products and the intentional transmitter testing required for radio systems.

You will always need to do the immunity/unintentional emissions testing but by using a certified radio module and staying within the conditions of its certification you can avoid having to do the intentional transmitter testing. [*]

3) If you are using a transmitter that doesn't have CE compliance then you must test it for compliance. Compliance to a given protocol is a very different matter, if it's 802.15.4 complaint then you may not need to perform any interoperability testing to sell the end product as such (I have no idea if such testing is required for that standard or not)

[*] This is admittedly a little bit of a grey area. In Europe you self certify which means in theory you don't need to test anything at all. However that wouldn't really count as due diligence if the certification was later questioned and you could end up in considerable trouble if you can't show reasonable grounds for believing you comply. 

However if you test your overall product for emissions and show that:
i) without the radio transmitter active it doesn't have significant emissions near the radio frequency
ii) you have documentation that the radio module has been tested and shown to comply under a certain set of circumstances and 
iii) you can show that you have treated the module in the same way as under the manufacturers tests.
Then it is reasonable to expect that your implementation will also comply. You can certainly get away with a far more limited set of tests, e.g. show that the peak power is the same or less than in the modules stand alone testing and it's hard to come up with a way in which you could then fail if the module passed. 

This link gives a reasonable summary on the state of modular radio approvals in different countries.
This link is specifically on the approval of products using ZigBee modules.