Before I answer those questions, I’m gonna yap about Kunzite’s lore (only the important parts.) Just to make it more clear

10 years ago, Kunzite was a student (a very smart one). Stel is one of the top student at his school. Kunzite don’t bother to make any friends, he thinks making friends is just a waste of time. Kunzite is a smart student, although he has a massive ego. Every person who challenged Kunzite ended up getting humiliated, what did Kunzite do to make that person face a miserable outcome? Kunzite is smart, but he’s not a good person. Kunzite had this one classmate at his school, the name of the classmate is Beryl Villaverde. Kunzite and Beryl had a competition on who is the smartest student at their school (since they’re both smart.) Kunzite will do anything to win this competition. Beryl ended up winning the competition, and Kunzite went mad. Kunzite never lost competitions like this, that’s when he gets his hatred of Beryl. (Kunzite is an asshole okay?)

Where were we? Oh yeah! 6 years later from that event, Kunzite received the gemstone of Ascendancy (how did he get it? I’ll get to that in the future.) Kunzite knew that with the gemstone, he’ll be better than the rest. Except that 3 (possibly 4) others also have gemstones, “how can I be the best in the world when 3 other peasants also have a gemstone?” This is when Kunzite decided to take down the other gemstone holders, stel wants to be the ONLY gemstone holder in all of the middle world. Kunzite uses manipulation to get what he wanted.

Now that’s all done, time to answer the questions.
Kunzite wants the gemstones so badly because he wants to be the only person who holds the gemstones and needs the power to take over the whole middle world.
The gemstones each have different powers and purposes.
The gemstone of Resistance is greatly used in battles, it gives you more defense and strength. It can give you a shield to absorb like over 80% of the damage idk.
The gemstone of Enchantment is greatly used when you know how to use magic. If you don’t know how to use magic, then it’s useless. However, this gemstone is very powerful when you’re an expert at magic. This gemstone basically buffs the magic spells you’ve already learned, like super buff. For example, if you have an ice spell, the gemstone made the ice spell do more damage and destruction. Idk, depends on the spells.
The gemstone of Sagacious just gives you more knowledge about others and the place around you. Sounds boring, but it’ll come in handy when you want to know someone’s secrets heh. Kunzite really wants this one, trust me
The gemstone of Ascendancy makes your influence way more effective. Easier to do manipulation. Kunzite had this one and oh boy he’ll go crazy with it. This gemstone gets stronger every time your manipulation was a success. Idk ran out of ideas.
There’s possibly a fifth gemstone but we currently don’t have any information about that.

Kunzite’s original end goal was to be on top of the world, ruling the whole middle world. Well, that is still stellars end goal, but he also wanted to take over some parts of the overworld and the underworld.

That’s all of the yapping, I ran out of ideas 🪂