relicencing and rebuilding : best practice?

First of all, you have to understand that the administrators will remove data from Odbl/Contributor Terms decliners and you cannot re-introduce them afterwards yourself. Second, there is a wiki page about remapping the data here : http://wiki.openstreetmap.org/wiki/Remapping

> Do I simply delete the existing 'bad' ways and draw in my own 'good' ways?
If you know them and use an appropriate source (like Bing imagery) for the position, then yes. But you cannot reuse the previous shapes, positions or information coming from decliners.

> am I able to copy the information provided by accepters to my new way ?
yes

> FOSM : I go and get information from it, and I attribute the source in my changeset, is that not OK?
No. See the first point above.

> FOSM : What if I only copy data added by 'accepters' and ignore that made by 'decliners'?
I don't know the details about FOSM excepted that it is a fork project going ahead with the previous license cc-by-sa. At the moment, OSM contributions are done under both licenses Odbl and cc-by-sa. That's why OSM updates are mirrored in FOSM but this should end-up after the deadline of April. Also the FOSM contributors do not have to "accept" or "decline" Odbl/CT's, so we cannot copy data from FOSM back to OSM.

From what I know the main reason to remove data contributed by users who did not agree to odbl/ct is not the licence, but the CT.
CT generally say that the contributor gives osmf licence to use the data and publish it under any free licence osfm sees fit. ODBL is a licence that specifies how the data can be used. It can be changed (to another free licence) without the need for all CT users specifically agreeing - vote of 2/3 majority required.

Whether you can or cannot use the old (CC-BY-SA licenced) OSM data is a different, more general question - Can you use any CC-BY-SA data as a source?

CC-BY-SA does not protect the database itself (that is the reason for ODBL). What is protected by it is the graphical representation. The BY part of the licence is easily fulfilled by attributing the source, SA excludes some use cases ad therefore makes CC-BY-SA incompatible as a source. That means you cannot directly use the graphical representation (copyrightable, licenced under CC-BY-SA).

Yet another question is, whether or not you can use the data ("a road goes prom place A to place B, let's transfer that information"). That depends on the jurisdiction and would require more complex analysis...

Short summary: What prevents you from using that data is mostly likely not copyright or any other law, but OSM's super careful policy regarding data use.
The important thing about any licence is that it allows something, not restricts it. If there was no licence, no one could use that data (with current IP law in force)

Sorry for highjacking this question with an "answer", which is merely a follow-up question.

I am a little shocked, that the fact, that much info might be deleted in several months, is not very well made clear on the main page. In fact, I heard about that for the first time now.

Will there be a central effort to contact "decliners"? Or should the local community do that? What if there is no local community? I am mapping in Georgia, and we are first of all only a small bunch, and second, prefer to add new map features instead of putting much effort into re-mapping big parts of the country.