What are warning quests

You'll notice that you have a little tiny icon next to your sharpness level. This is the area for buffs and debuffs. This particular one is a debuff, and it lowers your defense, as indicated by the black shield with a down arrow on it. Most likely one of those tiny insects gave it to you; they like to do that.

To clear it out, a Nulberry should do the trick. Or, you can wait until it goes away on it's own.

Slots are used for storing Jewels, and is done through the blacksmith, via the decorations menu. All Jewels give you an increase to at least one of your armor skills, and some will even decrease a skill.

Jewels are crafted through the same interface as weapons and armour, and require various monster parts or other miscellaneous items, plus a base jewel. You can get the base jewels from mining nodes (Aquaglow, Sunspire, and other Jewels), which then have to be crafted and attached via the blacksmithing interface. The blacksmith is also able to remove jewels from an item, which is non-destructive (you can swap jewels between armour sets).

While mining, and occasionally from quest rewards, you may receive a Mystery Charm. At the end of the quest you're on, you will be given a second menu after dealing with normal monster loot - the Appraise menu. It will reveal what your Mystery Charms actually provide, and allow you to select one or more charms and send them back to your equipment box. Charms are equipped in a sixth slot, independent of regular armour, and can sometimes carry +10 in a single skill, allowing you to quickly tack extra skills onto your equipment set.