Can I place rooms/equipment specific to non-alchemy professions in my Whiterun House?

Solution 1:

As @yx. said, you cannot get anything besides what Proventus Avenicci will sell you (the only "useful" thing is the alchemy lab) in Breezehome.

If you're looking for a location to sleep and store things in a non-respawning container that has an enchanting table, I highly recommend the College of Winterhold. For only 30 gold (to get into the College, which you don't need to pay if you already have the spell she asks for), you get a room in the College's living quarters (with a bed and a chest), which has an enchanting table and alchemy lab in the same zone.

Solution 2:

Its not possible to place a enchanting table into the house. I've purchased all the upgrades and the only thing is the alchemy table. I am unsure of other houses as I haven't purchased all of them yet. (Solitude one costs a whooping 25k gold)