Are there any LDS schools or orphanages besides BYU? Any in other countries?

I haven't ever heard of any and would imagine if they existed it would be all over the LDS publications all the time.

Southern Virginia University is not owned by the LDS church but is run on LDS principles by a group of Mormons. SVU is in Buena Vista, VA, where my mother grew up. She attended that school when it was Southern Seminary Jr. College, a non-religious school. I considered going to Sem when I was in high school because they had a dynamite riding team and I was really into horses. Sadly, sometime in the 1990s, Sem went bankrupt and these LDS businessmen bought the school. They've turned my mom's hometown into an LDS enclave. It's very sad. The building that used to be the barn is now a big basketball court.

I knew the wife of one of the bigwigs at SVU because her husband used to be the CFO at the hospital in the town where I went to college and she joined my college's choir. At the time, I didn't know anything about Mormons, but then I married a convert who is now, thankfully, an exmo.