Could ved be explained in the translation a little better? I find the words that it translates as do not correspond with the correct answer. It makes it difficult to know exactly how to use it.
You can see "ved" in this situation like a "currently". I'm currently eating (right now). In french we sometimes say "en train de [+ infinitive verb] .." (which could be translate by... "in the process of"...I guess)
"Har du tid til at købe ind nu?"
"Nej, jeg er ved at spise."
It's like the difference between "I eat" and "I am eating." This sentence is the latter.
It's to emphasize the fact that it's currently happening right now, right ? I guess in english it would translate by adding a few liaison words, like "right now" or ""at the moment" or something like that ? Am I wrong ?
There is no way the word 'er' is being spoken here.; is it standard Danish to 'swallow' this whole word in this construct?
It's extremely common. Danes tend to combine and swallow portions of, and entire words.
The previous translation of "jeg sidder og spiser" is also "i am eating". Are these usually used in different situations? Or either is fine when talking of currently eating?
Did you see @viktorbluhme's answer?
' "Har du tid til at købe ind nu?"
"Nej, jeg er ved at spise." '
That should explain it. Do you need further help?