Standing still, there is no way to tell via mundane means
Darkness vs Blindness
Being inside an area of darkness puts you inside a heavily obscured area. This is true whether the darkness is nonmagical or magical (as in the one created by Darkness).
PHB 183
Darkness creates a heavily obscured area. Characters face darkness outdoors at night (even most moonlit nights), within the confines of
an unlit dungeon or a subterranean vault, or in an area of magical
darkness.
All creatures inside a heavily obscured area suffer from the Blinded condition.
PHB 183
A heavily obscured area—such as darkness, opaque fog, or dense
foliage—blocks vision entirely. A creature in a heavily obscured area
effectively suffers from the blinded condition (see appendix A).
Silence vs Deafened
An area covered by the Silence spell makes a much more direct comparison to Deafness:
Silence
For the duration, no sound can be created within or pass through a
20-foot-radius sphere centered on a point you choose within range. Any
creature or object entirely inside the sphere is immune to thunder
damage, and creatures are deafened while entirely inside it.
And so, there is no way to tell.
Except...
You can leave the area of effect
Both Darkness and Silence create static, non-mobile areas of effect. An easy, mundane way to know is to walk in a straight line until you have walked a certain distance. If you are still blind, it's the Blindness spell; otherwise you will be able to see the area of darkness behind you. If you are still deaf, it's the Deafness spell; otherwise you will start being able to hear again.
Alternatively, you can cast Detect Magic
Blindness/Deafness is a necromancy spell, whereas Silence is an illusion spell, and Darkness is an evocation spell. If you could cast Detect Magic, you would be able to tell the difference between these schools.
You can also try casting spells
Spells which require a Verbal component fail entirely inside an area of Silence, but you can still cast them while Deafened. For example, you can use a Healing Word on yourself. If you regenerate hitpoints, then you must be under the Deafness spell.
Can you use Blindness/Deafness/Darkness/Silence as a tool?
On your final question: is it a tool you have as a DM? Yes, of course it is. You could set up traps and puzzles that require sight or hearing to be gone. Or you can have deaf party members due to the Deafness spell trying to communicate with the other non-deaf party members. It's fun (for you, at least).
Will the players feel hassled? That depends on them. If you would really like to spring it on them, I say give it a shot. But if you genuinely believe they will strongly hate it, ask them to be sure. The reactions of your players will depend on that particular set of players and is not something the people at this Stack can determine for you.
Your job is to present them with obstacles and puzzles to challenge them. This is just one of those ways to do that. So yes, it is within your toolbox if you want to use them.
Stone Casting Likely Allowed, but there is case for No.
The Reserve Ioun Stone only states that:
While this stone orbits your head, you can cast any spell stored in it.
There is no difference in casting language between the stone or a spell naturally, just that you can cast any spell stored in it.
However, there is a case against this with the requirement of expending a spell slot (see below.)
If allowed, this is an excellent way to expand the list of possible Contingent spells outside of the traditional Wizard spell list.
Next is to look at the requirements of Contingency
Choose a spell of 5th level or lower that you can cast, that has a casting time of 1 action, and that can target you. You cast that spell—called the contingent spell—as part of casting contingency, expending spell slots for both, but the contingent spell doesn’t come into effect.
What happens here is that you have cast both Contingency as well as the spell from the Ioun Stone (assuming it passes the criteria of 1 action casting time and targets only yourself).
Do note that this frees up the space in the Ioun Stone as the spell has been cast.
The spell cast from the stone is no longer stored in it, freeing up space.
The contingent spell is fully cast and just waiting to come into effect. There is nothing more needed for the spell to take effect other than the trigger provided.
To answer your specific questions:
Does having the spell stored in such a way count as a spell "you can cast"?
Yes, the language is identical between casting from an ioun stone or casting naturally.
Does the fact that the spell is stored in an item mean that it can't be cast as part of another spell as Contingency requires?
There is nothing to suggest this given the casting language is identical.
Is there any other reason why this would not work?
The main remaining concern is the requirement from Contingency of
expending spell slots for both [Contingency and the spell to be triggered].
If it is required for a spell slot to be used, then using the Reserved Ioun Stone will not qualify as there is no spell slot expended.
I think this is a bit of a stretch, but a strict RAW reading may preclude the use of the Stone with Contingency because it failed to expend the spell slot.
This concern is similar to Ring of Spell storing requiring a spell slot to be expended when casting a spell into it. Jeremy Crawford confirms that here
It requires a spell slot. A wand doesn't expend a spell slot.
Comparison to other Items:
Ring of Spell Storing
The Ring of Spell Storing also uses similar language and should be able to be used in this way as well.
While wearing this ring, you can cast any spell stored in it.
Hat of Disguise
This is an example of something that would not work with contingency. The language here requires an action to cast Hat of Disguise.
While wearing this hat, you can use an action to cast the disguise self spell from it at will.
Best Answer
The answers, see below for main source.
The continual flame has no effect on lighting in the area of darkness unless it has a higher spell level than the source of darkness. So only the 4th level continual flame would work in this case.
The torch doesn't matter as per this FAQ:
Yes, they can attempt to dispel or counterspell the continual flame spell, as per the respective rules.
Yes, the rules for a targeted dispel state:
Since deeper darkness has a target of object touched, the object must be touched in order to dispel it. Additionally, the rules for counterspelling state:
This means that while you do not have to touch the object to counterspell, it must be within the range of Deeper Darkness, which is touch.
Illuminating Darkness (Paizo Blog Post)