You can increase charm by completing side-quests (mostly townsladies), reading some books (boobleena vol 8) at study task. Full charm minigame is coming up next.
For the equipment quest, after you give the pictures, talk to him and you'll be able to craft the next equipment upgrade. Get the materials needed, you can buy them from the miner, Bedge, on the mines (day) or pub (night). As soon as you craft the item, Ramdo will forge new items and the quest will be done.