No, they don't obviously go into the combat pile. Most of these are general purpose features. The only unambiguously combat features are those that are directly connected with killing stuff. (Weapon profs, attack and damage bonuses, blasting spells and the like)
Metamagic for example has plenty of combat and non combat in it, and it all depends on what spells you take. Having Quicken/Twin/Empower does nothing for your combat capability if you don't have combat spells.
No, it is not, it isn't a clear cut dichotomy. For example, what do you make of something as simple as Magic initiate? It has obvious combat uses, but I tend to derive a lot of out of combat utility out of it, I've never taken it to improve the combat aspects of my character. To me, it isn't a combat feat, but to many people it is. In what pile do you place it? Should you place it in the combat silo, then we have fluffy not-combat feats in the same spot as combat feats, should it be on the non-combat silo, then we have a combat enhancing feat in a place where players shouldn't be able to derive any combat power from. We could then decide to get rid of it, and all of the ambiguous feats, but at that point we are just plain losing options. Leaving feats -and features- unclassified opens up more design space. Once you have clear cut silos, you no longer have the option.