It should be - almost.
The point of the question is to teach you that this is the correct way to say 'I am working'. The verb obraich has, in effect, two verbal nouns
Bha an gleoc ag obrachadh 'the clock was working (functioning).
Bha an duine ag obair 'the man was working (at work)
I said 'in effect' because obair isn't actually a verbal noun. It is a noun meaning 'work' used as a verbal noun.
The word ag/a' is a special spelling of aig used before verbal nouns. Thus we know obair should be treated as a verbal noun here
aig obair 'at work'.
ag obair 'working'
There would be little practical difference in spoken Gaelic but they are written differently.
It's not that shall isn't used anymore, but that it isn't used just to indicate the future. It is used (in the way the old grammar books say it should be used other than in the first person) when you want to indicate a sense of defiance:
Cinderella shall go to the ball
I shall come home late (even if you don't want me to)
I think this was called the optative mood but I'm not sure. Because of this specific meaning, I now avoid it when I simply wish to say what will happen, so I would consider only will correct here.
i could be wrong, but i think "bidh" here denotes the future in particular. like the english sentences "i work on fridays" and "i will work on friday" are not the same thing, right? one of them refers to your present-tense employment situation, the other refers to what you are going to do this friday in future tense. to me, nothing in this sentence shows that you'll be working every friday.
jellyman74 is actually correct. Bidh does mean 'will be' literally. But this construction is also used for the habitual present, as there is no other way to do this. So you have to learn that every time you see this construction, you have to think which makes sense, or if they both make sense. They deliberately set some questions with the habitual present meaning, such as this one, but of course they have to accept both translations unless there is something in the sentence that makes one impossible. Note also that the example in the link shows that Gaelic does not distinguish between Friday and Fridays in the way that you demonstrate in English.
Due to a complicated sequence of events over the last 2000 years, we have ended up with the situation where the independent and dependent forms are pronounced almost identically, but spelt differently:
- Bidh mi I will be
- Am bi mi? will I be?
- Nach bi mi? will I not be?
- Cha bhi mi I will not be
Originally, the two forms would have been the same, but the dependent form must have lost the last syllable - hence bi. But the independent form retained the second syllable - hence bithidh, but then lost the second syllable at a later date - hence bidh.
Firstly, please don't assume that everyone speaks the same way that you do. If you think your sentence is used in the correct meaning by a significant number of people, then you can argue for its inclusion, especially if you identify who would use it. It is most unlikely that the question writer would simply have used bad English for no obvious reason. It is far more likely that they wrote what was good English in their dialect.
There are two separate issues here. One is the difference between Friday and on Friday. This is simple. The first is American English and the second is British English. With these differences, they generally accept suggestions of an additional translation if you point that it is reasonably widespread such as (as here) standard American English.
As for the simple present I work as opposed to I am working, in this one-off (i.e. this coming Friday) context, as opposed to habitual, this is not something I have heard in any dialect of British English, and I am not aware that it is used in what is generally considered Standard American English, so if you could identify what dialect you have heard it in, that would be really interesting. To my ears it sounds more like something that a speaker of a continental European language would say.