I changed all my lines and sheets to dyneema and the difference is huge especially with the jib sheet.
As for diameter. I think that the boat is supplied with 6,8 and 10 mm lines. I found that the smaller diameter lines don't work too well with the winches, so would suggest only using 8 and 10 mm.
As for the reefing lines, again I would suggest an 8 mm system. Those lines are under huge loads and I'm not sure that a 6mm line would work too well. We had an 8mm line shear in two once as it was cut by one of the reefing blocks shattering under load.After 3 seasons my reefing lines are looking fairly worn and it's one of the jobs to do during winter .

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Be aware that some of these lengths may be incorrect; I've experienced that the kick, clew outhaul and cunning were to short. I unfortunately do not recall the correct lengths for these.

Nope, I mainly use 10 and 12mm Dyneema. 

I would not use 12 mm lines for reefing. 10 mm is more than enough. I think that if your budget is tight , then you don't really need dyneema.

If you have experience in reefing a Hanse then this next bit will be a little boring for you .for this my apologies :)
We found that reefing can be quite a challenge. The outhaul, backstay tension, and vang tension need to be off. The boat needs to be head to wind and you need to experiement with the main halyard vs reefing line tensions.
If there is even a little resistance on the reefing lines the block on the sail will jam against the boom and continued reefing pulls the side off the block caused casastrophic failure. The same applies to the mast base blocks which should have springs underneath them to keep them permanently upright. This again minimises the change of the block jamming with the line sideways against the wall of the block and shattering it.
All this learnt from bitter experience. But in answer to your initial question; once set the reefing lines will not need further adjustment like a jib sheet and so stretch is not really an issue. Also, when set a 10 mm line secured around the boom will be more than enough to keep a reefer sail in place.
Hope this helps

For the reef lines I still use the yard-delivered 8mm polyester; they are not being used at all  - so far I have only reefed my main once...

For the halyards I use 10mm (Dyneema), and 12mm(Polyester) for the Gennaker.

I have not considered to replace all ropes to Dyneema, as some of this not necessarily gives an improved perfomance - such as the halyard for the Gennaker.