From my understanding Messianic Judaism is a form of Christianity that believes in Jesus Christ as the Messiah, but strictly following Jewish law and commandment?
We believe the Law/Torah is relevant to all believers, Jew and Gentile as outlined in the scriptures. When one says Jewish law, that's an incomplete statement. Yes it was given to a redeemed nation in Israel, but was for all believers as the scriptures plainly state. As far as strictly following the Law, well that's up to each individual. And yes, there was a difference between man made rabbinical laws, and God given laws.
How widespread is it? Also what do they call their house of worship? A church? Synagogue? Temple?
Don't know how widespread it is, but it is a growing movement for sure for one reason or another. As far as what we call ourselves, I tell my kids it's time to go to church. Some people get hung up and try to distant themselves from anything "Christian", but it don't matter to a lot of people. It's a place to worship The Lord.
What are their typical practices compared to Christianity?
As with anything, there can be a huge divide even amongst different Messianic congregations. Some Messianics/Hebrew Roots have teachings that Christmas and Easter is based on a pagan holiday and shouldn't be observed. Even if it had its roots as such, taking a day to acknowledge the King of Kings birth is honouring and glorifying him I find nothing wrong with that. It's the only time of year Jesus Christ is sung on the radio without it being used as a swear word. Even unbelievers get up in arms about taking Christ out of Christmas, so why would teachers preach their congregants against it? Don't make sense to me. Hanukkah and Feast of Purim are based on Jewish events and history that even Jesus observed, although they weren't instructions or commandments like the spring and fall feasts.
Main differences are observing the feast days and the Sabbath. Passover is coming up next month. It's a Sabbath that we come together to praise and worship The Lord, sing, dance, fellowship with others and remember Jesus was the Sacrificial Lamb for all. Yes, a terrible thing to be "under the law."
Traditions vary from place to place as in their service agenda. Worship is first, bless the kids underneath a tallitz before Shabbat School, read the news about going ons in Israel and what's happening in the believing community whether Messianic or Christian. Generally all believers nowadays are being persecuted and need prayer. Break into small groups and pray. Have the Torah scroll taken out of the "Ark" and it's walked around and people can touch God's Word and place it upon their heart or on their lips while singing Thy Word is a Lamp.. Then there are 7 Aliyah's/readings from the scriptures that 7 people are invited to stand up and read. Then the Rabbi will have the teaching. Then break for oneg (eat) then leave. 4 hours usually, but easily 4 of the quickest hours of the week unfortunately.
As I know people will say we aren't under the law, and cursed if you are and so on. I can only tell you what I have lived and experienced, and if this is what it's like to be under a curse, then bless that curse and may it never go away. Passover is coming up and Jesus followed it absolutely. Think about attending a Passover meal. I'm sure you will have a different perspective on this so called Jewish feast.
I could go on, but I would be happy to try and answer any other questions you may have.