The short answer: yes, you need quality. Quality in eeeeverything. With a better quality bone saw you can make better boards. Even if you can't hunt boars yet yourself, some people go round hunting them and leaving the skeletons by the river, so boat around for a while and see what you can find (hopefully without becoming a target yourself). Or trade with a neighbour, of course. You need decent survival to get decent bones (max q 56 from a boar), so if your survival isn't that high yet, wear two sets of the best nettle clothing you can make to boost it.
Are they q30 *fresh* tea leaves, and they become lower q when you dry them? If so, you need a better herbalist's table. Otherwise, I expect you need better quality water to make the tea, and probably a better quality cauldron to make it in. Sorry

One of the things I didn't know about mining, is that it's not possible to mine within 50 tiles of the cave entrance (if you mean a cave and not a minehole that someone built). So the very basic 'how to mine' facts are: buy Mining. You will then get the Adventure: Mine option. When you click this, your curor turns into a little pickaxe, the same as for Adventure: Destroy. So go into a cave or minehole, and if it's a cave walk more than 50 tiles from the entrance, get your mining cursor and click on the cave wall. Either you will start mining or you will get a message that the rock is too hard. If the rock is too hard, go away and get more strength. If you can mine, probably there won't be any ore there anyway. If there is ore, it will appear in your inventory. If there is no ore, rocks will drop onto the ground instead. If there is no ore, walk further and try again

Good luck.