Hi Mattie
You're right about the first one - the comma goes before you close the inverted commas. Check in any published novel and you should be able to see this principle in action.
The second question isn't as clear-cut. Either (a), (b) or (d) could be correct, though not (c).
If you put a an apostrophe after writers', it implies an element of ownership - the circle is owned by the writers, in other words. That may well be the case, of course.
But equally, it would not be wrong to say writers circle, without any apostophe. In this case, the word writers is simply functioning as an adjective. An analogous example would be sports hall. There is no apostrophe in this, as sports do not own the hall (obviously). The word sports simply clarifies what type of hall it is. The same could be said of the word writers in writers circle or writers group.
Writer's circle would not be correct. Putting the apostrophe here implies that there is only one writer, and with just a single member I don't think you could really describe it as a circle!
Finally, writing club is of course fine, and avoids any need to agonise over the use or otherwise of an apostrophe!
Hope this helps

Nick GM