Populi!
I try to find a word in Latin which couriers this specific sense: right, just, the very; and still found nothing.
I mean that I can find it in many another languages: right here, just behind, in this very place; tam artında; pryamo za, srazu za; they are very equal.
If I try to translate thus adverbs directly, they lose this tinge of the intensiveness.
You'll have to choose different words for precise meanings. One option is to use the intensifier ipse (which is functionally what "very" is doing in your third example). The dictionary gives a good analogue to your examples:
ea enim ipsa hora acceperam tuas litteras, "For it was at this very hour that I received your letter." (Cic. Fam. 7.23.4)
Another option is modo, which is used adverbially. You get phrases like semel modo ("only once"), non/si modo ("not only"/"not just", "if only"), and nunc modo ("just now"), though you don't even need the nunc to express that: it can mean "just now" by itself. Plautus Rudens 3.3.29 has "sedete hic modo* ("sit right here"), which matches your first example exactly.
