You do not "arrive" in Germany officially. That doesn't happen until you have a place and you present yourself down at City Hall. You will then register as being a resident of that address (not a concept that exists in the US) and they will sort you out then.

No real limit on luggage on the train, but with kids, they tend to not be able to handle much luggage on their own. Have the company ship your stuff if possible.

Of course you can visit before. You are a tourist for 90 days. I HIGHLY recomment that the both of you go appartment hunting together at least 30 to 90 days before you are planning on moving. You can google moving to Germany and find absolutely masses of information. Most will target the military but it is easy to weed out the parts that are not related to you.

I must admit, your hubby's employer doesn't appear to be very on the ball about informing you what you need to do. Where are you planning on putting the kids in school? What town are you planning on living in? Where is the end-client for your husband? Banks are downtown but their IT departments are north of Frankfurt. Not sure why your husband would get local medical coverage and you not, but this is often and arrangement between the company and the host country. Make sure his contract includes tax equalization coverage and assistance doing your German AND US tax returns becuase you are going to have to file both.