Do the gems, shapes, color have any significant meaning?
I'd like to ask a specific question in relation to this, the Hungarian crown with its "tilded" cross, did that actually exist, and did it have any meaning?
I think it depends on the crown. The Austrian Imperial Crown for example even has pictures of Emporer Rudolf II on it, showing him on multiple glorious occations.
edit: oops, I misread this as /r/AskReddit. I hope someone more qualified than me can give an in-depth answer.
Speaking to the crowns and coronets of British royalty and nobility, each title has a specific design that is the official symbol of their rank.
Barons have 6 large silver orbs (called pearls) on a plain band.
A Viscount has 16 orbs around the rim, touching each other. The band of this rank and all above it up to Duke has the metal patterned to resemble inlaid gems, but doesn't have actual stones.
An Earl has alternating metal strawberry leaves and orbs on raised stalks, 8 of each.
A Marquess has 4 strawberry leaves and 4 large orbs alternating around the rim.
A Duke has 8 metal strawberry leaves.
For all ranks, the metal used is silver-gilt.
Moving up to royal crowns, those are a bit more unique/custom, but the heir will have a single arch crossing from side to side, and the monarch will have two arches at 90 degree angles, creating the distinctive high topped crown.
The sphere on top of those arches represents the world, and is found on the crowns of emperors in particular. The cross atop the arches indicates a Christian monarch. Cross on top of sphere on top of arches indicates a Christian Emperor.
The particular gems used vary, and often are swapped around over the life of the crown and may not have particular meaning. Some do, of course, have meaning - a special stone from a given country of their dominion for example - but that is not codified.