Open just means no restriction on techniques.  Using Restore option to somehow checkpoint skip is something that's impossible in Time Attack mode.  That alone should warrant an update to the rules specifying this abuse.  

In the case where it can be abused, going out of bounds in Time Attack mode causes the vehicle to be unfinishable and unable to count a lap.  In practice mode, this same action with restore on can allow a lap to still finish.  Same case scenario, 2 different results depending on the game mode used.  If it is proven that a lap only counted because of the effects of restore, then the lap should be discounted.

I should note that I have no experience in how spaceflying works but I think a resonable person would think a run that can't be replicated in Time Attack mode shouldn't count.

What this guy said ^

Although in the end, the opinions of people who actually spacefly are more important then a lowly pleb like me.

some testing on emu

https://www.youtube.com/watch?v=jTdh8jtV9vQ

https://www.youtube.com/watch?v=4DO1HFK9j_c

Restore on lets you do things not possible in time attack

Pretty much, yeah. See midiman's second video above for the idea - apparently what you have to do at the start of the lap is more complicated (clip through the track floor), but if done right, you don't even need to cross the first checkpoint. You just cross the start line and then go off course. So it's a 3-4 second strat (albeit not an easy one) which works for pretty much any track. Looking at the current spaceflying WRs, this means the strat would improve around 16 to 20 (of 26) lap WRs, all using the same strat which disregards everything about the track except what's immediately before/after the lap line.

midiman's first video above demonstrates the exploit which Faizer found. Port Town Cylinder Wave is one of the few (maybe the only?) tracks which allows you to finish the lap below the lap line. In this case Restore doesn't seem to be a factor in tricking the checkpoint system, but it does allow you to carry your post-off-course inertia into a lap completion. This allows you to finish the lap at a slightly lower point than you could without Restore, which can give a slight advantage, since having to maintain height slows down your spaceflying.

Here's how I'd answer the questions in the OP:

1. Yes, about 16-20 Open ladder WRs (based on how many WRs are above 4 and 3.5 seconds, respectively) with the checkpoint exploit, and then the PTCW exploit makes it 17-21. Not easily in general, but for WR standards I guess it'd be relatively easy. Maybe more to the point, non-Restore strats wouldn't stand a chance for most of those courses. For the other main categories, not that I can think of, since they don't allow checkpoint skips in the first place, and I don't think going low at the PTCW lap line would be relevant.

2 + 3. I'd say what's possible in Time Attack mode. I guess banning Restore abuse is comparable to banning CPU boosts and handicap boosts in GP and Versus modes, respectively. So do we want a "finish the course/lap as fast as you can, in any mode" ladder? There is precedent for this (SNES forces you to play many tracks in GP, and MV saves times from GP), so that's not exactly unreasonable. It's a bit more out-of-the-box for GX though, since GP, Versus, and Practice times never get saved. All things considered, I can see the 'Open' naming going either way, but all else being equal I guess I'd vote to just keep it as is - Open being defined by what's possible in Time Attack.

4. No, I think having Restore On is fine as long as it doesn't activate during the fast lap itself. With video proof, we should be able to tell if it does or not.

Here is our current rule proposal which will be applied to all of the ladders. I think it's a good idea to dis-allow any runs where the machine breaks down before crossing the line with restore on is because there's always the possibility that the run would fail if restore was off or it was done in Time Attack mode. The speed overflow bug could potentially happen, and of course the machine could fall off course without crossing the line or hit a kill plane. While we could allow broken down finishes in Practice mode with restore on and check them in a case by case basis, there will certainly be times we just can't know with 100% certainty whether the machine would successfully cross the line or not in Time Attack mode.

Rule proposal:

If you have Restore turned on in Practice mode, your machine may not break down or go off course during the fast-lap.

These two restore exploits that has been found so far are banned in all ladders

1) Going out of bounds before completing the lap, but still complete the lap as your machine is being restored - https://www.youtube.com/watch?v=jTdh8jtV9vQ

2) Doing the following exploit where you can fall of the course immediately after the lap begins, restore right before the start/finish line and complete the lap in potentially under 4 seconds. - https://www.youtube.com/watch?v=4DO1HFK9j_c

^ The above rule proposal will be established if there are no objections in the next 3 days (72 hours). Postponed for now, since new points have been raised in Discord (#fzgx).

There's been discussion on whether the rule proposal a few posts up is a too strict and would potentially invalidate some of the current flap PBs and future ones. None of the max speed flap WRs done in practice mode with restore enabled break down before the finish line. It's a valid point and it would be not an ideal situation to deal with. It is likely that there would be a fast lap where the machine breaks down right before the finish line during a rail slide while restore is on.

Instead the rule could just list out the exploits that cannot be used like so:

If you have Restore turned on in practice mode to set a fast lap, the following exploits cannot be used to set a fast lap

1) Going out of bounds before completing the lap, but still complete the lap as your machine is being restored - https://www.youtube.com/watch?v=jTdh8jtV9vQ

2) Doing the following exploit where you can fall of the course immediately after the lap begins, restore right before the start/finish line and complete the lap in potentially under 4 seconds. - https://www.youtube.com/watch?v=4DO1HFK9j_c

I think that'd be fair. Cases like the 10k speed cap are still a concern for "does Practice have a slight advantage over Time Attack?", although at least it becomes a (relatively minor) consistency question instead of doing something impossible in TA.

Also, a direct ban of the two exploits you listed is probably the most intuitive rule. There wouldn't be a need to ask what the rule is trying to accomplish.

 We're overcompilcating this, ban the usage of Restore option that isn't replicable in Time Attack, it doesn't take a month to figure this out

Then, to clarify, do you think breaking down before the line with restore on would make a fast lap invalid?:

I'd like to wrap up this issue soon too, but you can't appeal to haste to push a particular stance. We're considering opening a dedicated Discord channel for each rule discussion from now on (in a separate FZC Discord server), so we could potentially start with this one if we're having trouble getting this wrapped up quickly.

 If we are going with that wording Zewing, then that would put into play what I mentioned in the previous post about how having restore on would allow fast laps to be completed but would potentially fail if time attack were on in other scenarios. This can especially happen in courses like Mobius Ring and Loop Cross where there are kill planes on the walls of the tunnels, and other courses where the machine may go over the wall and fall off if it were done in Time Attack. 

Plus because we are allowing restore for fast laps, there is the potential case of a fast lap that is only possible to achieve by having more than one boost lap to set up which wouldn't be possible in Time Attack mode. If we implemented your version of the rule, then such fast laps would not be allowed. 

I get that these is a very niche circumstances and maybe something we can just not bother thinking about. However I think it's important that the rule we implement leaves absolutely no room for doubt in every possible scenario. If most people think this is being unnecessarily nitpicky and has no real chance being an issue in the future then we can go with Zewing's proposed rule. Otherwise I think it's safer to ban the specific methods that we don't want in the main three ladders.

Setting the 3 day (72 hour) timer again to establish AKC's latest rule proposal. Feel free to raise any new (or newly clarified) points until then.

 It has been over 72 hours. The rule has been implemented. The fast lap run has brought about this discussion is now disqualified.

 Updated my time to show my best run without the exploit