Before I was born my mother was a Mormon, and I assume she was a registered member of the church---her parents were Mormon (although they may have belonged to some kind of offshoot of the main church). When I was baptized in the Lutheran Church, just before I was confirmed (about 12 yo), I recall her telling me I was also baptized a Mormon.
Question 1.Do Mormons practice infant/young child baptism?
Question 2. Would I be a registered Mormon
a) if I was baptized one?
b) if I wasn't baptized one?
Question 3. If the LDS church doesn't practices infant baptism do any of its offshoots?
Question 4. Would I be a registered Mormon if my mother belonged to an offshoot?
1) No, Mormon's practice a believer's baptism, youngest age this is possible is 8.
However, Mormons do "bless" a newborn baby, which is an official prayer and naming on behalf of the baby (not baptism).
2) If you were baptized in the main Mormon church, then you are on the church records as a member. If you were blessed as a baby, they would also have record of that event, but you won't be a church member. Either way, you can contact your local church any simply ask (it does not matter that the events did not happen where you live now, all mainstream Mormon churches are linked, like a public school system). If you'd rather do things online, ask at mormon.org/chat and they should be able to help. If you want, you will be able to look things up on your mother as well.
If you or your mother were involved with an off-shoot church and not the main Mormon church, then the main Mormon church would not have records of it (the off-shoots are completely different churches and their baptisms are not recognized by the main church). I'd suggest you contact them.
3) In the Book of Mormon, infant baptism is bluntly declared unnecessary and contrary to the way of God. So, the main Mormon church (consisting of 99.98% of Mormons) does not baptize infants (though they do bless), and of the 0.02% remaining, the 3 largest subgroups I'm aware of likewise do NOT practice infant baptism.
4) See #2.
If you wanted to know more about this, I would suggest talking to your mom about it. If she has passed on, we can still help you out.