I've updated your times to include real time.

There's currently no marriage category on the leaderboard purely because nobody has ran it yet.
Currently emulator is banned for both of the wii games due to the inaccuracy of the emulators, this can be changed to fit in with the rules of other games in the series where emulators aren't totally accurate, in which emulators are allowed but hidden by default.

The glitch is done by picking up a power berry at the same time you do one of the tired animations. Then you move to another screen and press A so that a clone of yourself appears. The next time you change screens, you should have a power berry floating above your head, any items you eat on this screen will count as a power berry, but once you eat at least one and change screens it will disappear.
As for whether or not it is system specific, I don't know, but I think it is unlikely.

Using any glitches, including this one, are allowed in runs

I'm not sure the numbers for converting the times is correct, instead wouldn't it be for PAL to NTSC just multiply the time by 0.8333 (25/30) and for NTSC to PAL multiplying by 1.2 (30/25).

Either way, I'm not necessarily for nor against this, I'm just not sure it's necessary.
It's something that happens with a lot of games, but there aren't any games/leaderboards that come to mind that take into consideration framerate conversion. But that doesn't mean there shouldn't be any room to change this standard either.

I can definitely see where you're coming from, but I feel like adding an extra step, could potentially make running the game look unappealing, especially to new runners. However, the alternative is to, in a way, force PAL runners to either move to emulator, or purchase a new console/game, just to get a comparatively good time, which isn't very inviting for new runners either.
Also, what is the calculation you're using for converting PAL times to NTSC?

Emulators for both platforms are allowed

When you're going to sleep and the screen starts fading black, hold down L, R, select and start.

I've added Lumina as a marriage sub-cagtegory to the leaderboard

More friends of mineral town, and a mrriage category for each candidate has been added.

I've added the Marriage category to the leaderboard, and added your run.

If you're able to come up with other good categories for this game, then there's a good chance they will get added. The problem is that besides marriage, there aren't that many other "good" options besides a couple of the ones you mentioned. Honestly, the best thing to do is to just run a category you think would be cool, and then once you have a run, the category will most likely be added to the leaderboards.

Best Ending counts as the "Happy Family/Rancher" Cutscene. This is a small description of it from a very good/detailed guide:
"REQUIREMENTS: Married, 2 children, 900+ happiness, 10 Power Berries eaten,
10,000 G, own 1+ cow, own 1+ chicken, hugged dog 100+ times
This is the "best" ending in the game. Jack will be sitting on the front porch
of his house with his wife, parents, two children, dog, and horse. They all
wave at you as the screen fades. You will receive this ending even if the
second child was not yet born, but your wife was pregnant with it."

999 Ranch Master Score would be the requirement for a 100% run (with the number of ending scenes being debatable).

I've just updated the google doc in the guide, so it's exactly like the notes/guide I use when I do runs.

From what I can tell by looking at what other games allow, Bizhawk is fine to use.

I've just added the category.

Yes you can.
The game currently doesn't have it's own leaderboard, but if people ran it or there was 'demand' for it, I can add the game to the site, and set up categories for it, similar to Wonderful Life.

First of all I'd like to clarify that the rules were actually added by me, but they were basically taken from that thread. I also feel like I should note that they're not exactly "new" rules, existing runs used these timing methods, and apart from a few frames (which are generally fine, people can't always stop timers frame perfectly), the runs are perfectly fine, and I've only re-timed them frame perfectly, because this kind of thing has come up.

So after re-timing the three runs you mentioned above, these are the times I have gotten:

JonahSpeedRuns - 1:57.98
Bernacaz - 1:58.26
Aspercio - 1:58.91

For future reference, re-times should only be used for runs that look off, not every single run.

I think having a few google documents for the different games is a pretty good idea.
I don't know how exactly you route categories, but I just end up taking a lot of notes, which could easily be transferred to google docs, to be viewed and possibly edited by other runners

I think runs that involve going into the later game would be really interesting. Not sure how long a full game run would take, but it would probably be really long

In terms of deciding your child's career, I know that the different child of each girl will slightly sway for one career more, but I don't know how much. Celia's son is more interested in farming, Muffy's son is more interested in being an athlete, and Nami's son doesn't really care, as long as he's not an athlete. From what I've read on HM wikis and sites, your child's career is mostly influenced by making certain friends and buying your child certain toys.

I think as a possible full game run, aside from the child's career, would be a run in which the player has to reach the end of the game but also has to meet certain objectives, maybe something like having a certain amount of profit made, either by the end of the game or each year, by fully expanding the farm or something along the lines of that, just so the player actually has something to work for.

A slightly longer run for the game which I've been working on for awhile now, is an All Animals run, which runs into the second chapter of the game and involves doing things other than sleeping.

The only other possible categories are things like getting all the tools, or befriending all of the villagers, maybe even something a bit more silly like all fishes, crops or recipes.