Creating numerical columns using a group by add to fact table or create as a dim table

It depends on the nature of your facts. For example if you have Orders and Shipments then you could theoretically keep them in the same fact table.   But if you have Sales and Quota then you cannot combine these facts, they have to stay separate.  And there should be NO link between the fact tables !!!

Another thing to consider is the size and growth characteristics of your fact tables. Some will be slow growing, others will keep growing massively every day and you will want to think about  partitions and aggregations etc.

Having numerical columns to link between facts and dimensions is considered good practice as it helps to improve the join performance.