What happens if you increase the duration of Seven League Stride?
This is probably one of those cases of "troupe veto it because it doesn't work within the rules of the setting." If you really want to force the oversized peg into the appropriately-shaped-but-not-accommodating hole, I'd say you pick a destination when you cast the spell and can teleport to it at any point within the spell's duration as long as you meet the Range qualifiers. This does have the rather significant effect of basically porting in "Contingent Teleport" from D&D, with most wizards possessed of the necessary skill casting it calmly before any journey (with an AC to their lab or something) so that they can flee from intense danger without risking a botch. Granted, characters can already pull something akin to this off with magic items or spell mastery, so the effect wouldn't be too gigantic.
All in all, nothing breaks either way, but requiring that it stay Momentary is probably the most sensible thing to do.
Please don't do that, it gives me a headache! 
IMHO the obe thing that this would under any circumstances not do is to allow the teleport to be 'held' until needed. This is more or less what Tethered Magic does.
I would say a Duration above Momentary for teleportation is inapporpriate and won't help. Just like longer Durations for Craft Magic won't do you any good either.
The spell constantly works, constantly teleporting you to the designated destination and thus "pinning" you to it. You cannot move or be moved from the destination, as you're constantly re-teleported to it.
I can't see a use for that, but that's what I'd suggest.
Possibly use as a unecessary high-level "jail" spell. Maybe for an entity which can teleport herself ?
She moves wherever she can, and at the end of the round, the long duration teleport spell bring her back to the destination of the TP spell.
It could potentially be a specific solution for an entity that cannot be trapped by ward, chains and solid walls.
Such a trapping spell needs not be unnecessarily high level, if using the lowest possible base for a mere 1 pace teleport?
If the entity can cover a large distance (because of whatever power/abilitie she has), the lowest possible base will fail to bring her back. I don't have my book with me, but I believe that the base level even for a 5 paces TP is not negligible (level 15 ?).
I would believe that if the TP spell distance is shorter than the distance to cover, it simply fails. It won't TP 1 pace at a time until it reaches its final destination. Usually spells work or don't, but don't do intermediate results (botch and Finesse failure excepted).
Also, if you want to use the spell to trap the entity, you can base the spell on Leap of Homecoming, with range of Touch or Voice (+1/+2 magnitude), and Moon duration (+3 magnitude). As soon as she is within spell range, the mage can teleport her to what will be her prison, where ever they are when the spell is cast (across regio being the exception). Quite a useful spell at the end, but high magnitude, so Penetration can be a problem.
This is correct.
It comes directly from the definitions of durations in the core book.
What about a Concentration duration version of Seven League Stride? Would that allow you to teleport someplace and then automatically be sent back to where you started when you stop concentrating or would it just teleport you there and keep you there until you stopped concentrating, at which point you could move away normally or would it do something else?
Second option.
As far as I can tell.
Please note that it is not a different scenario from what is described above, really.