I did the first part so far (website.net -> website.com) around 5 weeks ago and it went well and most of the links have been moved but google is very slow with removing old website index and by the looks of it will take another 2-3 months at least to complete the move 100%.
My question is can I do the second part now as well (website.de -> de.website.com) and move the translated version too or should we wait until .net to .com is completely done? The problem is that this way it would take way too long and we plan to do a site redesign soon on a new domain as well.
I was advised to first do the domain moving and then after a while do the redesign and url structure change.
Also, GWT does not have a support for moving website to subdomain, will this be a problem ?
you can create and verify another site in GWT for the de.example.com hostname. then you can use the "Change Address" option in GWT to move from the gTLD domain to the ccTLD domain. then you can geotarget the de.example.com hostname for users from germany if that is your intention or otherwise leave it untargeted for worldwide german users.
as far as google is concerned, your example.de content is already filtered for searches on google.de since most gTLDs are automatically geotargeted. if your intention is to geotarget de.example.com for germany, then redirecting that content should essentially be seen as a move independent of your example.net to example.com content redirects.
last time i did a large scale redirect, the old urls were getting deindexed at the rate of about 50% per month. not sure if that still holds true and it wasn't a domain change so it might not apply directly to your situation.
the hard part will be when you change the url structure, since you will want to redirect from the old url structure on the example.net and example.de domains directly to the new url structure on (de.)example.com rather than relying on a chain of redirects. you also want to avoid a 301 redirect from the old hostnames to a 404 response for the request on the new hostnames.
In my experience, if its already been 5 weeks since .net redirect; and Google has started to pick the signals well you can always go ahead and make the redirect for .de as well. Just remember the usual stuff to keep the XML sitemaps of both sites submitted to Google for faster processing and if need be (and you got the option) increase the crawl speed of old site post redirection from WMT.