It would be good if all alchemy tables had an alchemy bag on it (like in Breezehome) that automatically linked to the table. so you wouldnt need to empty the bag everytime u wanted to do some serious alchemy, then put all the stuff back.

Yes.

This.

That is a great idea, funny thing I didn't find the alchemy bag on the table in breezehome for about 2 weeks. Also, it would be cool that if you put in a potion recipe that it would automatically add those known effects to the proper ingredients.