* Does the player's character have an uninterrupted minute of time to cast the spell?
Yes, otherwise you abuse the
fair play notion.
* Does any potential intruder come within 8 hours, or do they turn up (say) 8 hours and 5 minutes after the spell was cast?
The DM may
(1) Handwave the long rest as all good with no RE roll due to pacing, RL time-constraints, nothing prepped...etc.
Conversely can this be done in TB or is the table forced to participate as per the game rules?
(2) Unload a prepared encounter whether it be to for balance purposes (resource attrition), to inflect the danger of the terrain, the encounter is part of exposition ...etc
(3) Utilise RE to determine potential encounters.
In either of these three instances, the Alarm spell is not necessary for them to take effect.
* Does a potential intruder come within the warded area, or open the warded portal? Or do they sneak around the warded portal, or inspect/attack from outside the area?
Once the potential intruder is established, the DM, via guidance of the monster fluff and stat block determines the approach taken by the intruder.
* If the caster (and friends) are asleep, and are woken by this spell, how much can the intruder accomplish while they rouse themselves?
See below
On its fact, this spell looks like something that a player could use to help control the risk environment for their PC. But on closer analysis, it turns almost entirely on GM decision-making that is significantly unconstrained.
All of this depends on GM decision-making. That decision-making is largely unconstrained, except by some pretty loose notions of "fair play".
Given your background in law do you feel the legal term "reasonable person" is largely unconstrained and a pretty loose notion?
I accept that a
reasonable DM engages in
fair play.
If not, then either the DM is young and/or inexperienced and/or there are other issues at play.
By choosing to use the spell, does a player actually affect the risk to their position in the game?
Yes of course. One need not use an Alarm spell, a party could set up a rotational watch, or select a location that could minimise the risk of potential intruders (i.e. ranger input)...etc
The party's actions have great importance in a game where
fair play is expected.
One, I would think, only question it if they did not enjoy the style and/or believing that a reasonable amount of
fair play could not be achieved.
Even TB relies on
fair play to some extent, however miniscule.