I think wait or wait a minute is okay, and would sound softer, more polite, if you followed either expression with please; however, you also need to follow it up with an expression like I didn't (quite) understand that, or I didn't (quite) understand what you said; I didn't (quite) get that or I didn't (quite) get what you said. All of the preceding expressions could be preceded by Excuse me? and, in fact, when speaking to native English speakers, Excuse me is often sufficient on its own to communicate your intended meaning. Alternate, more casual expressions--which should also be followed by the same kind of explanatory follow-up statement to make your intended meaning completely clear--are: hang on, hang on a second, hold on, or hold on a second.
In the United States, one term is suitcase student, and an institution which has many such students may be known as a suitcase school. For example, consider this 2013 New York Times article about Central Connecticut State University. Connecticut is one of the smallest states, and CCSU is an institution sponsored by the state government, so the great majority of its students are from areas less than two hours away (which is extremely close by US standards), and so this pattern is prevalent.
Almost half of Central’s 7,700 full-time undergraduates live in dorms or near campus. But most vanish each Friday, joining the army of undergraduates at “suitcase schools” around the country who desert their campuses on weekends.
They head home for the same reasons suitcase students always have: favorite meals, moms (and now dads) still willing to do their laundry, high school friends and sweethearts, and jobs. The refrain “There’s nothing to do on campus” is self-fulfilling. …
Moore, Abigail Sullivan. "Off Off Off Campus" in The New York Times, Jan. 31, 2013
The article is full of other suitcase terms, including suitcase culture, suitcase mentality, suitcase legacy. It refers to a student for whom life at the university residence halls is temporary, not a true home; therefore, they pack a suitcase of clothes, as if going on a vacation somewhere.
I wouldn't consider this term to be commonly used, as most colleges and universities are either traditional residential institutions or commuter schools, where only a very few students or none at all live independently on or near the university campus. Surprisingly, I found no results for it in COCA. In Google Books, however, they go back to at least the mid-20th century, e.g.
One problem that is bothersome today is the "suitcase student," who leaves campus on Friday afternoon and returns on Monday morning. Treudley, Mary Bosworth. Prelude to the Future: The First Hundred Years of Hiram College. Association Press, 1950
Ole Miss remained a pleasant headquarters but scarcely a community of scholars. It was, as the expression went, "a suitcase school." Lord, Walter. The past that would not die. Harper & Row, 1965
Best Answer
There are a variety of words that can accomplish this goal. Most of them don't imply that the object can still move, but none of the ones I'm giving you imply that it can't. If you want to imply that it can still move, you could easily just add "right now", implying that at other times it may move.
"Still" — This is one of its meanings, and probably the simplest word to use here.
"Stationary" — This word means the same thing, though it sounds a bit more formal.
"Stopped" — This one implies that it had been moving at some point, which for all of your examples is most likely true. It won't necessarily start moving again, though. This word can also be applied to things that aren't motion, but I think it works well.
"Unmoving" — This just means not moving.
"Motionless" — This one implies that there is no movement at all, so it might not be exactly what you're looking for.
And, as Au101 said,