I am wondering what they are used for..those crystals in the battle shop. Also if anyone knows what scrolls are the best at level 3

Can't really help with scrolls but as for those Crystals...

You can add them as mods to your weapons. The elemental ones go good with certain weapons, and modding those weapons against certain challengers gives a slight boost in the weapons icon damage. Example: If your weapon does 10 icons of Earth and your opponent doesn't block a lot of that icon, modding your weapon with the Earth Tear Crystal gives you a little boost, the Baguette gives a slightly bigger one.

Same goes with the Defense ones cept with those it helps BLOCK the icons a little better. Granted if your weapon blocks say 60-90 icons of certain elements while having more can help it's not really recommended. Unless you're going up against a challenger who does insane amounts of one icon type.

Now there's a few other crystals that help and are not elemental.

Thief crystals help boost the likely hood of a weapon stealing (if said weapon has a low percentage of stealing this boosts the chance by only slightly)

Healing Crystals help boost your weapons heal percentage at random throughout the battle.

Freeze Crystals work best if a weapon isn't 100% freeze. Cause there's no point adding this if the weapon always freezes. This is better left to weapons with a low chance.

Natural Armor Crystals give you a blessing when activated during battle. This gives you a 2 of every icon block and prevents opponents from stealing your weapons if they have that ability.

Critical Strike Crystals boost the chances of your weapon doubling their damage, though granted they aren't that great. I can't offer any more insight because I don't know all that much about them since I rarely use them.

Now your weapons you can mod from your armory page (having your crystals in your inventory) Some weapons have 1 mod slot so you're limited on what you wanna add but you can change it any time (but you don't get those mods back, once you change them the crystals are gone forever) Some weapons you can't mod at all. Weapons that are generally tier 11+ have 4 mod slots. Also Demi and Godly weapons have 4 mod slots usually so they add more variety and such when you mod them.

Now I left a bunch out so hopefully someone else can explain anything that I've missed. I apologize if I've confused you, feel free to ask questions!