Your MetroPCS phone must be unlocked if you want to use it with another SIM card. If you bought your phone from them, it may be locked. if your phone bought from them isn't yet paid off, they may not unlock it - but if the phone is paid off, they should. Just ask them. They will give you an unlock code, which you won't use until you insert another SIM card the first time. Then you type the unlock code once after powering up the phone with the new SIM, and that's the only time you'll ever need to use the unlock code.
You won't have your MetroPCS US phone number while you have another SIM card in place. You'll get a new phone number (e.g. a UK number if you buy a UK SIM card) until you put your old SIM card back in.
The EU has done away with most roaming fees for residents of the EU. However, tourists can usually take advantage of the free roaming too - but not in every case it seems. Some mobile companies may require you to use the SIM for a couple of weeks in the original country before they will enable the EU roaming (an attempt to make sure you are a resident). I have read of anecdotes about some UK SIMs having this enforced. I have a Dutch Vodafone SIM, and I have never had a problem roaming - in fact, I have never even used this Dutch SIM in the Netherlands - I bought it on eBay last year and have used it in France, Italy, Slovenia, Spain, and Portugal - but not in the Netherlands.
In any case, just buy a SIM in the first country you arrive in - buy it at a mobile store, and ask about the roaming. If for some reason it doesn't work when you get to the next country, then just buy another SIM there. You will need to take your passport with you in some countries to activate a SIM card.
If you want to make calls home to the US for free, even to landlines, install Google Hangouts on your smart phone (and also the Hangouts Dialer app if you have an Android). You can make free voice calls to US numbers from within the Hangouts/Hangouts Dialer app, while you are on WiFi or with mobile data. Just make sure you add the +1 prefix to the front of a US phone number first. Also consider a free texting app like WhatsApp or Google Voice.