1st part..all depends on where you are,( where you are incorporated or whatever form your legal entity is ), where they are,( where they are incorporated or whatever form their legal entity is, and where they registered their "trademarks" ) who your registrar is ( which is relevant as it it also says where the registrar is )..these all affect "jurisdiction", ( to a lesser degree also who your host is may affect the outcome )..some places are better than others for your position as regards "disputes" over domain names..in some you may have a very good case ..
How on earth can I transfer to a new domain and keep the rankings the site has? It ranks position 1 for most of the keyword in google and bing, and only a couple of positions lower for other keywords. If we hand this domain over I can't exactly do redirects so what can I do?
not much ..but then if the worst happened you wouldn't be handing over the domain ..just the name, and it is possible that as the domain structure would be your copyright that they could not use it..nor keep the urls that the inbound links come to..in which case any victory they might get would be "pyrrhic" :)
You may even have acquired certain rights to the domain name(s) due to your prolonged use of them ..but that depends on who is doing the judging and where and by what laws..as I said in part 1..
flip side is that, in certain jurisdictions ( despite your "disclaimer" on site ) .you may be considered to have been "passing off" ..due to the use of their name and product, as they may have "acquired" rights to have their name and products considered to be their "trademark" even before they formally registered them as such..
See more than one specialised lawyer..any advice/ comments etc here is from "nicks" on a forum ..and is worth what that is..everyone's mileage will vary