It should be - report it.

Beteg means to have an illness, indeed. Talking about rosszul is more feeling unwell.

'Ssz' is a double-sz, so it's pronounced like a long 'sz'. If you double a digraph (or a trigraph), you only double the first symbol: cs -> ccs; gy -> ggy; zs -> zzs; dzs -> ddzs; and so on.

You just have to watch out with compound words, like karosszék - armchair, which consists of the parts karos - armed.. erm, "with arms", and szék, chair. There is actually 's' clashing with 'sz'. But since those sounds are difficult to pronounce so closely together, it's mostly spoken as an actual 'ssz' anyway.

It's conjugation! Hungarian is full of that:

• vagyok - I am
• vagy - you are
• vagyunk - we are
• vagytok - you (pl.) are

(The verb "to be" is a bit strange in Hungarian, since "he/she/it is" and "they are" usually aren't translated, but you rather say something around the lines of "A ház zöld" - "The house (is) green".)

In gy your tongue is lying almost flat and your lips are "smiling"

It is between 'd' and 'i'

It's at least very odd. What you want to do with this question is finding out someone's condition: sick, or not sick? So rosszul is the focus point here. And in Hungarian the focus appears in front of the conjugated verb: "Rosszul vagy?"