[Coldsaturn]

Don't feel discouraged, protocores are the bane of every player's existence, even the ones who are pros at this. And leveling them up is a pain.

You can see here the basic actions you can do in the protocore page. On the bottom left of the page you can select so that every time you get a blue level protocore or even a purple level protocore, it is automatically discarded 



And here what you see from the Decompose button



The enhancement page works in the same way with the filters. I can make a visual guide for that too if you need it!

How to swap protocores?
In the most basic sense, once you have selected your cards for the battle, by tapping on a card you get the button to Boost your team. On each card's page then when you click on the protocore it has on, an entire list of all the other eligible ones will open up. If a protocore you want is already on another card you can still decide to equip it, you'll simply get a popup window asking if you want to unequip it from the other card.

HOW to swap protocores?
Heh. We're all learning. 
Consider that my abysswalker solar cards are also sitting with only purple level protocores. That's just a matter of being unlucky when core hunting. Don't be scared to experiment a lot with which protocores you're putting on, and use the button Details (top left of the page where you can Boost your team cards for the battle) to see how your team stats change based on what you've equipped. ATK needs to be up so save cores that have that as main stat or at least as a substat somewhere, Crit Rate is also important (especially if you're not matching stellactrum), DMG boost to weakened is also important (especially if you're matching stellactrum), Oath's strength is nice, Expedite Energy Boost is so good if you find it (it helps you use more active skills during the battle).

Ultimately, the best way to learn is to experiment. Resources in this game are limited but still just a matter of time before you get back what you've eventually wasted, so get your hands dirty. It's possibly the only way to really get a feeling for what works.