For the moment it is a big discrepancy between what is possible and what is actually seen. The Mode S implementation on the ATC side is far from finished and it depends very much which center/airport you talk about. Specially since most countries have differing (their own) ATC systems still...
When it comes to enhanced mode S downlink parmeters (the speed, level, heading) its just about only London that have access and soon Maastricht. (Feel free to correct me if im wrong it might be that my knowledge is not up to date.) The exact parameters seen will likely depend on the implementation - some may see more than others even after the implementation is done. (since this is likely system dependent and of course limited by the standardised airborne capabilities)
TAs has as far as i know never been a suggested downlink parameter, a big discussion about the pros and cons about RA downlink is still ongoing but to my limited knowledge no one has this ability yet.
As for warning systems i would assume that most radar equipped european ATC providers are using some kind of Short Term Conflict Alert (STCA). This provides roughly 2 min prewarning before a loss of separation. The TCAS doesnt care about separation and have in cases even contributed to losses of separation - its the last system in the safety net and just aims to miss...
My 2 cents...
Edit: The STCA is radar derived and not affected by airborne equipment.