No, you will have to significantly adjust encounter difficulty as time goes on with these powers as written
I caught your original post, I'll address the specific crystal in the block. Long story short - you are going to throw you campaign way outa whack when you introduce those into your campaign at 10th level. And since your planning on progressing it, they will be getting 1 or two more crystals per level as you reach 18th or 20th level (or more if you cap out sooner).
You should tone them down, and either allow them to grow with the caster (Base Bonuses = 1/2 your proficiency bonus), or have their powers "Unlockable" later as the campaign unlocks with either a McGuffin or research into these Legendary/Artifact level baubles.
Everything here is opinion. It's my take on it. Can be thrown out. =D
Without knowing the composition of the party - I don't know if these are balanced or not. Party composition and tactics have more to do with party combat effectiveness than +1 weapons and raw levels. But one thing is certain, you will need to start throwing in either more, or stronger monsters at the party than their CR would allow as they collect more crystals.
The +2 spell level is a bit - unclear. Don't make it cast as if using a spell slot 2 levels higher. Don't give this to your warlock, or anyone with a half casting spell progression. This is essentially a 4-6 character level boost to the wielding caster and does not affect all classes equally. So at level 10, your looking at trying to effectively combating level 14-16 Casters in your challenge ratings, while your fighters and rouges are still level 10.
A +1 or +2 to bonus modifier to casting ability score (Not Attribute) would work well. Similar to a magic weapon. The attack rolls and spell DC's would go up without effecting counterspell or adding a ridiculous number of damage dice / number of affected creatures when casting with higher spell slots. +2 spell levels would best be saved for the artifacts "Final Form" when your characters are at God tier levels of play. It would be assumed you could throw a creature at the one caster with all the crystals and the fighters and rouges will still have something they can do.
There are 8 crystals, make attunement a requirement. 1 Crystal per player, make them choose
Imagine your monk, or your cleric, or your bard with the bonuses of every crystal. This will overbalance a single character and ruin inter party balance in regards to combat effectiveness.
At 10th level, you need the crystals to remain relevant through the course of the storyline... so I would suggest toning down many of the outright powers, and make a widget or widgets you can drop crystals into (Bracer / circlet / staff / Amulet / Ring). The widget either give a minor LATE GAME boost to empower the crystals and then allows more than one attunement?,
Better would be a single widget you have to start putting things into. The final widget can only be used by one person, and only for a short amount of time. Then the party can choose who wears the widget and risks going all Vecna on the party, and who is holding one of the crystals in the "Crown of the Lich King" or something silly like that.
Abilities. You don't have to have them with god tier abilities out the gate. The one true ring from LoTR was an invisibility ring until it woke up. You can up the power quotient with research or as quest rewards. But I would say anything at will with unlimited uses - should be thrown out no matter the power level. This leads to game breaking abuse, where you have to do some crappy game breaking things to your party to challenge them. The Rod Of 7 Parts quest from 2nd Ed D&D ran into this problem and ruined a lot of friendships when it was published. So be careful and keep it toned dow.:
- Abjuration - Remove Dispel at will - change it adds proficiency bonus
(or advantage, not both) to dispel or counter spell rolls.
Spell slots = resources. No resources = instant player abuse.
Dispel magic every 5 feet anyone?
- Conjuration - Alternately you can say saving throws to resist the
wielders banishment attempts are at disadvantage.
- Divination - Fine as is.
- Enchantment - I would say make this function more like a ring of
storing. The ring has the concentration slot and can hold
concentration. After words to put a new spell into it requires a
long rest. So you can still have "Double" concentration for the big
fight, but your no longer risking stacking abuse.
- Evocation: - Meh balance. Potential for your warlock to pump out
double ridiculous spell damage every turn. Its a free average 9
damage (or basically an extra attack) + Cantrip damage (Eldritch
blast... 3d10+ch for your warlock). If they cast using a bonus
spell, they can only cast another cantrip during their turn. So
yes, this has a balance mechanic built in.
- Illusion: Put a time limit on this sucker and a number of uses per
rest. This one gem - has essentially turned your battle field
controller into the guy sitting in the corner twiddling his thumbs.
I'll make an illusionary wall of force in a sphere around the entire
enemy encampment.... Now it's real... and that only cost me a
cantrip or 2nd level spell slot? I'll make the illusion that the
floor is nothing but instant glue 2 1/2 feet deep... This one gem
will single handedly shut down 99% of all encounters and fights.
Give it late game or don't give it.
- Necromancy - This one is easy - give it a specific number (like 1/2
your level) of zombies that can be raised... and specifically
state that this gem does not allow you to control more zombies than
you normally would. Requiring raise dead or the like to re-assert
control after the long rest using spell slots. Keep the million man
dead army in check... at least until you get the widget and they can
fight gods. Otherwise, I kind of like it.
- Transmutation - This one is actually perfectly balanced. Mind you
it's infinite gold and wealth - but combat wise it allows you to
change swords to match damage vulnerabilities... Now does this work
to change 1 cubic foot of material (the enemies head) into lava? Or
just their helmet... or just the stone brick above their head... How
about "Sun Plasma"
At 10th level, definitely tone all of them down. And don't leave your non-casters out of the mix with stuff they can do. The gems requiring attunement and only being able to attune to 1 gem unless they have a widget are going to be critical for keeping game balance until you can get them up into the 14 / 16 /18 level power breaks, where it won't hurt as much. Give them meaningfull options of "Choosing this crystal, or that crystal, but not both" and the power levels will stay in check, and it will still add a lot of fun flavor. Be careful not to fall into the 3.5 trap where spell casters do EVRYTHING once they hit 14th level, and your non caster classes are just meat shields or the peanut gallery.
Okay that's all I got.