Do German universities take mid-career international students for PhDs? Do German universities (specifically, Technical Universities) take mid-career professionals from other countries (i.e., the USA) for PhD studies? 

I am trying to grasp how that process would work - or if it would work - for someone with family &amp; in their mid-30s.

N.b., I am aware that the system is different, i.e., Funded PhD position chances for international students in Austria. 

My field is computer science, if that matters.
Yes, that is definitely possible (if you have a Masters degree as JayFromA mentioned).

Normally professors have their own funding and 100% control about who gets accepted into the PhD program. This means you directly apply to the chair and not to the university but if the professor is willing to pay you your other background does not matter.

The computer science community in Germany is very international (especially the TUs are very proud of this) and it should be no problem if your German is not that good. 

If you do not have stipend your salary is fixed though and there is no room for negotiations (and its not really competitive to industry work). There will also be no relocation funds or anything. Teaching is normally included in your duties so you can not upgrade your pay with that.

The good thing for people with family is that most programs offer "Individualpromotion" which means you do not do course work but research independently (with the help of your supervisor). This is normally more time flexible and useful if you have small children.