OK, a little bit more background..... Verizon, except for the 4G phones, uses a technology called CDMA (as does Sprint). This does NOT use a SIM card, so your phone would work fine in the US if you took the card out. (You might get a message about No SIM, but everything, voice, data, text would work fine). The SIM card is only needed for the other major technology, GSM, and that is what you would use in Germany. So unlocking the phone etc, doesn't impact your US service at all. When you return to the US, it will work fine, whether you leave the German SIM in, or replace it with the original one.
SD card. Leave that in. It's used to store data for applications, photos, music etc. You will need it in if you use the phone camera. Using the SIM won't impact it, so it's absolutely fine to leave it in, and various things will work better.
Unlocking the global feature: this is only if you are using the Verizon SIM abroad. What they do is activate the SIM and allow your phone to make international calls. If you are using a prepaid SIM, Verizon never gets to see the traffic, the phone has nothing to do with Verizon, until you return to the US.
What the unlock code does is to allow you to put a non-Verizon SIM in the phone. By default, GSM carriers in the US, and Verizon on these phones, lock their phones so you cannot use them on other networks without their permission. Basically Verizon wants you to use their SIM because they can make a lot of money! With a prepaid SIM, unless you suspend the Verizon service, you just continue to pay the monthly charge, and all calls/data/texts are charged to your prepaid SIM. So, you need to talk to Verizon Wireless global and ask for them to unlock the phone so you can use a foreign SIM. (You need to be precise here, as some reps won't know what you mean. In particular, you don't want the code to unlock the screen, nor the PUK code for the SIM. Some reps are much more knowledgeable. Ask for Global Services) Not sure how long it is for the Droid 3, but they are often 8-16 digits. When you place a new SIM in the phone, you will see a prompt, and you just enter those digits and you are done forever with the unlock. Doing a factory reset, or even more extreme things (SBF), doesn't relock the phone.
Activating the SIM. You will probably buy the SIM preloaded with some airtime. The store, especially if you go to a carrier store, will help. You may need to call a number to activate, or the purchase process may activate. The box the SIM comes in will have the phone number printed on, and you can also get it displayed from menus on the phone once the SIM is inserted.
I don't know how long you will be there, if it is for any length of time, ask about top-up procedures. You can do this online, but US credit cards might not work for this, so best to get top-up vouchers or something if you expect to use up all your original prepaid time. Many stores will sell you top-ups (as do many ATMs, but don't know how well this works with a US card).
Now to be fair this is the "happy story" version. Generally, if you get a current SIM, things should work OK, and the phone will automatically read needed information from the SIM to allow data to work. Otherwise you will need to set up an APN, which is fairly easy but writing it out makes it look intimidating. I can give you the information if you want!
To save battery, when you get the SIM it makes sense to change the network mode to GSM: Look for something like Settings>Wireless & Networks>Mobile Networks and then select GSM/UMTS. The reason for this is if you leave it at the default Global setting, the phone searches for a Verizon signal (and it won't find one!) wasting power.
Re Voice Mail. Yes, you can dial your usual number (with a +1 in front from your phone). When you get your greeting, press #. You will then be asked to enter your password etc and you can listen to your messages. There are probably other ways of doing this, but I find this the easiest.
Thanks