The mining point - In Nophica Wells I've counted 30 different points, only 5 are ever active at a time (Prospect always has a total of 5 for the area). For leves I've only counted 5 separate points for each one. The same mining point can be revisited more than once as long as you visit enough other points between each visit, I'm not sure of how many that is but I'm thinking two between each one as I'm sure I've rotated between three points in a small area before. After a certain number of visits the deposit collapses, when it says "nearly depleted" on Lay of the Land it will only last one more visit. As mentioned earlier each mining point contains its own set of loot, though the sweet spot of ore is often found around the same area for multiple mining points it is not necessarily always the case.
Exposed Ore slider - Though SE says it alters what ore is available I have always got the same results in Nophica Wells no matter where I put it.
Remainder Bar - This is your first clue to what ore you are attempting to mine. Usually the higher the bar starts the more attempts you get to mine the ore but it's not always the case, for instance both Raw Sphene and Raw Heliodor start around 60% but the former gives you 4 attempts where the latter only gives 3, the latter also can't be mined with one attempt on the sweet spot. Most likely more than one ore will start the same on the remainder bar but if you're lucky all of them will have sweet spots around the same area.
Strike Meter - Should know where abouts you should be aiming here, if you're lucky every possible ore is around the same area otherwise you may have to try two or even three different areas. Problem I had in Bloodshore grade 3 area, both Iron Ore and Blacklip Pearl start around 70% on the remainder bar, Iron Ore's sweet spot is around the 50-75% area where the Pearl's is around 10-30% area. The Iron Ore can be mined first time but the Blacklip Pearl needs the sweet spot to be hit twice, if I start around 60% I'm likely to get Iron Ore first time but if it's Blacklip Pearl it leaves me with two more strikes to mine it, if I don't get a good second guess and hit the sweet spot then it's lost (also just missing the sweet spot the second time too). Obviously the best way is to aim for the Pearl first since mining the Iron Ore is easier.
Sweet Spot - I've formed a theory on this too. Why can you mine certain ores first time where others you can't? There's also been times where I've been able to mine an ore first time and times when it needed two attempts when I've been the same rank. And the very rare occasion where I've hit the sweet spot three times before mining the ore. Can think each ore of having a life bar, the "easier" the ore is the smaller life it has. Also the sweep spot isn't a point but obviously an area, and within the sweet spot is another sweet spot where you do more "damage" or perhaps it's a gradient with the most damage in the middle and the least on the edges. So for the "tricky" ores you hit the sweet spot but don't deplete the ore's health the first time you get the "you hit it but are unable to extract it" message (or whatever it says).
Quarry Points - On a side note I'll explain these quickly. Quarry points never deplete, they're always found in the same area they just move around in that area. I've found three different areas for quarrying in Nophica Wells and you only need to visit one other point before revisiting the same one.
I won't bother sharing my results since it'd take too long to write out, anyone mining the same area can make their own results up

Edit: Update for the update. What I've noticed so far is that the loot has changed for each point, getting more of a mix and stuff I only got up to grade 2 I'm now seeing in grade 4. Also the difficulty of ores has been changed, Gold Dust and Mythril Ore are easier (appearing around the 60% mark on the remainder bar) where uncut gems such as Raw Sphene, Lapis Lazuli, Heliodor are harder (appearing around the 40% mark). Ore health seems to have been fiddled with as well, I can no longer get Iron Ore with a single strike.
What does this mean? Besides my old data now being mostly useless the wider variety of ores makes it harder to predict what I'm aiming for and thus makes mining a little bit longer and sometimes less successful. Also a bit less profitable with more of the lower grade ores being tossed into the higher grade areas now.
The new system they've put in is kinda pointless. How it works is it basically tells you where the same ore you just mined is on the Exposed Ore slider, higher or lower, but you just mined it on so there's always going to be the chance of it appearing on your current Exposed Ore location. I'm not sure if the Exposed Ore slider does now give different results as I'm concentrating on just one location currently.