I asked Aela to buy my furnishings but she just took my gold and walked off. I have waited 20 in game days and so I got slightly impatient and built half of the house myself. Now my question is , will the rest of the furnishings ever arrive or am I bugged?

It seems to vary quite a bit, and some people report that they are not getting it at all, while others report that they get some pieces after a long time, then new pieces starts popping up after a while. Seems quite strange.

I haven't looked into the script though, so I do not know how it works.

Yes...just now around 3/4 of my decor popped up l but not all of it.