Yes, all single letter words are attached to the word following it, not just "wa". Words such as "كَ" ("ka", meaning "as") and "بِ" ("bi", meaning "with") are also attached to whatever word follows, with no space. It is not a "dialectal difference" as has been suggested here, the Arabic dialects doesn't even have standardised writing systems. In Modern Standard Arabic, i.e. what Duo teaches, there is never a space between single letter words and the word following it.

Yes no space between the two

as far as i know, whether or not there is a space is a dialectal difference