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The key to finding the price of any magical item is on page 549-550 of the CRB:
"The formulas only provide a starting point." and "The easiest way to come up with a price is to compare the new item to an item that is already priced, using that price as a guide."
With that in mind, the first thing to do is spell the item out.
A magical ring that imparts sustenance, and allows the wearer to recall one 1st level spell, one 2nd level spell, and one 3rd level spell a day.
That's effectively six levels of spells, plus sustenance. The Ring of Spell Storing holds 5 levels of spells, which is similar to what this ability is doing, but not quite as powerful.
It costs 50000g.
An ad hoc adjustment to add one more spell level, and I'd put the price of that at about 60000. Tack on sustenance as a completely different ability, and you've got 3750g.
Cost to create is 31,875g
Going by the estimating magic item gold piece values chart, we need to determine what the most appropriate numbers to use would be. The example given for *bonus spell* is a pearl of power. Looking at that example, we can see that the pearls of power didn't receive a modification for a *slotless* item.
So, we'll start with the basics.
Ring of sustenance - 2500g
Bonus spell 1 1000g (1*1*1000)
Bonus spell 2 4000g (2*2*1000)
Bonus spell 3 9000g (3*3*1000)
Now, we modify these. The bonus spells become charges per day, so we divide each value by (5/1) or 5.
ring of sustenance - 2500g
1000/5=200
4000/5=1000
9000/5=1800
Now we modify the item for multiple different abilities.
ring of sustenance - 2500g
bonus spell 1 200*1.5=300
bonus spell 2 1000*1.5=1500
bonus spell 3 1800*1.5=2700
We look at the total market cost, 7000g, or 3500g to make. Now, does this seem like a reasonable cost for an item that can reproduce three pearls of power on a daily basis? Nope, it's not a reasonable price, so we discard it.
Logically, the final item should cost more than 16500g market, since it is significantly better than owning each item individually. With that in mind, 63750g is a much more suitable market price.
when you consider that you hold a magic sword, a magic wand, a magic rod, and a pearl of power, I would say yes "held" counts as a slot.
an example of slotless would instead be an ioun stone.
Just my opinion though.
Sorry to burst your bubble but you won't be able to enchant the ring until 9th level. See below from the PHB and not the Bolded Section.
The second bolded part is just to point out that you can'e bond an object, enchant it, then sell it and bond a new object. Not that anyone mentioned that, but I predict it's coming eventually.
A wizard can add additional magic abilities to his bonded object as if he has the required item creation feats and if he meets the level prerequisites of the feat. For example, a wizard with a bonded dagger must be at least 5th level to add magic abilities to the dagger (see the Craft Magic Arms and Armor feat in Feats ). If the bonded object is a wand, it loses its wand abilities when its last charge is consumed, but it is not destroyed and it retains all of its bonded object properties and can be used to craft a new wand. The magic properties of a bonded object, including any magic abilities added to the object, only function for the wizard who owns it. If a bonded object's owner dies, or the item is replaced, the object reverts to being an ordinary masterwork item of the appropriate type.
Edit: I stand corrected. I just double checked and the level has changed from 3.5. My mistake.
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The ring of spell storing requires you to cast the spells into the ring first, and allows you to cast them back out of the ring at a later point.
The effect is very similar to pearls of power.
Following the suggestions posted at the top of my previous post, it's the closest magical ring to the effect you are trying to garner.
You're focusing too much on the math. The math is just the beginning of the process.
But to address your questions anyways:
the divide by 5 part comes from changing the consumable pearl of power effect into a per day effect, making it a 1 charge per day ability, which is a modification to the base price of spell level squared x 1000gp.
multiple different abilities cost "multiply lower item cost by 1.5", so the highest cost is considered the "base", with the lower cost values receiving the 1.5 increase.
For the example you've got listed, you haven't accounted for the change from a consumable item into a permanent, reusable effect. You've only accounted for the abilities being stacked into one item, not for that ability being usable more than once ever. Make sense?
As for the "slotless" element, look at the prices for the pearls of power, and compare them to the formula "Bonus Spell". They fit that value exactly, which means they weren't originally modified by "slotless", which means that you can't un-modify them.
Slotless, btw, generally counts for something that is worn without taking up an item slot. It basically allows you to wear two belts, or two cloaks, or whatever, as long as one of the two items is a *slotless* item.
Your final total, from your example, is 23,500g. Or, in other words, you've price your ring of sustenance that lets you recall a 1st, 2nd, and 3rd level spell each day, close to the same price as a ring of invisibility, or wizardry (1). At its best, that ring of wizardry is providing an additional 5 1st level spells, or 5 spell levels. Your ring is providing six spell levels, including up to third level spells, and also provides sustenance.
That makes it significantly better than wizardry (1).
However, nailing down an exact price is something you'll have to discuss with your dm. It's not something you can do just with the formulas. They only provide a starting point to the process.
The section on crafting magic rings just comes out and says that rings are hard to price, and you should do your best to compare them to preexisting rings.
So find a ballpark range that you're comfortable with, and makes logical sense to you, and then pitch it to your dm. He/she will make the final price call.
As far as I can tell Pathfinder magic item creation rules don't really make a distinction between what type of abilities should be on rings vs. on wondrous items. I think you can safely add any ability you would find on a wondrous item to a ring for basically the same cost. The only cost adjustment is going to be the +50% for adding additional abilities. So I think the originally discussed ring would work out to:
9000 gp - Pearl of Power 3 (start with the most expensive ability)
+6000 gp - Pearl of Power 2 (+50% for an additional ability)
+1500 gp - Pearl of Power 1 (+50% for an additional ability)
+3750 gp - Sustenance (+50% for an additional ability)
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20250 gp market price (10125gp to craft)
That's my understanding of the RAW cost. If I were DMing I would not add the +50% for extra Pearl of Power abilities because they are slotless items to begin with.
I think a Ring of +2 Int would just be 4000 gp market price (2000 gp crafting cost)