An assumption is technically something that must be taken for granted in order for an argument to go through. Some assumptions cannot, in principle, be proven. For instance, there is probably no way to prove that anything exists outside of my own mind, but I assume this because otherwise I would quickly die as a result of walking front of a non-existent car.
Less fancifully, if I thought that physics was a good and useful thing, then no matter how much I might doubt it, I would be forced to assume that the physical world exists if I wanted to be a physicist.
"Presume" has about the same denotation but also the additional connotation, as mentioned in Webster's, of confidence. Note that to say someone is "presumptuous" commonly means that someone is overly confident of their assumption.
As mentioned above, I think in most contexts today "suppose" is used rather to express a certain amount of doubt about an assumption, and in that sense has the opposite connotation to "presume".
In this sense you might think that "assume" has relatively neutral connotations, while "presume" and "suppose", as commonly used, have roughly opposite connotations. I think that's about right.
I can't think of many terms for this... all I can think of is a crossing or railroad crossing (Merriam Webster).
As for the "red-white" thing I would call it a gate or railway/railroad crossing gate - very descriptive terms, but that is what I would use.
As for your sentence I would say "At the railroad crossing, when the gates finally lowered, it was obvious I would be late for the party".
Check out the "Rail crossing warning signs" from Wisconsin, there might be other resources from other parts of the English speaking world?
AFAIK, barrier is more common in British English for the "gates" talked about above. Australian English i have heard of booms - but about these two I'm not the one who should be asked ;-)
Best Answer
The terms are roughly synonymous, but do have distinct uses that set them apart from each other as well. They both point to classes of vehicles, however the complete range of vehicles that would be encompassed be each term form distinct but overlapping sets.
Firstly car can refer to objects that aren't automobiles - railway carriages for example:
Secondly automobile can be used as a general classifying term that is inclusive of vehicles other than cars (and not inclusive of non-wheeled, non-self-propelling instances of "car", such as airship gondolas etc.) as per:
source: http://what-when-how.com/automobile/general-classification-of-automobiles/