True, but it's not bad to know how they translate. I had a Hungarian friend named Gabor that insisted he be called Gabe since he didn't like how people pronounced his name.
This is true, especially if they are going to have us learn the translations. Should be reported.
The sentence "János nem jól" doesn't have a verb, but "János nem jól van" is incorrect, because you can't use "nem van", we use "nincs" for that. See in detail and a bit better here: http://www.hungarianreference.com/Van-is-exists-omitting.aspx
Both true, but not quite why I was asking the question. I was thinking about how the to be verb "lenni" is typically only used in the third person when referring to location/existence or posession such as "fiam van" or "ott van az auto;" however sentences where description is involved like "Az az alma piros" omits the lenni verb. I see it in my magyar angol szotar, so I don't question the validity of it. The reference Bence shared is helpful. It's because jol is an adverb rather than an adjective.