1) Most missionaries in the United States, Canada, and Japan have iPads now (though not all) and they are beginning to test Android tablets in some missions.
2) Missionaries are able to install apps created by the Church, which includes Gospel Library, LDS Music, etc. as well as an Area Book / Planner app produced by the Church. I don't know how free they are to install other apps, but I assume they would need permission from their mission president.
3) Missionaries don't receive any extensive training on how to use Gospel Library, other than the in-app help/tips, and help from their companions or members.
4) Yes, they have full access to Gospel Library, which has content in 107 languages (including the Book of Mormon in 66 languages so far).
5) Gospel Library for Android supports having two windows of the app up at the same time in split screen (so you could have the same chapter up in two languages), but only for Android 7+. Missionaries with Android tablets will most likely be running previous versions of Android, so they aren't currently able to do this, and Gospel Library for iOS doesn't support split screen where the same app is on both sides of the screen. So, no, this isn't currently possible for missionaries without a third-party app.
6) No, this would be technically difficult or impossible to implement, since it would require sophisticated machine translation. Currently, when something is highlighted, Gospel Library knows (for example) that the highlight is in verse 7 and that it goes from word 13 to word 17. If you were to highlight the phrase "I will go and do" or just "go and do" in 1 Nephi 3:7, then switch languages, somehow the app would have to map the English "I will go and do" (words 13–17 in the verse) to the Spanish "Iré y haré" (words 10–12 in the verse). It becomes even more difficult if you highlight a vague word or phrase that doesn't translate exactly. If you were programming an app with this requirement, a workaround would be to only allow someone to highlight an entire verse, at which point you could highlight that same verse in every language.
Samuel Bradshaw • If you desire to serve God, you are called to the work.