So I've begun doing swings Every Minute On the Minute, and I enjoy it. I also know you are not supposed to aim for the 'test standard' time(10x sets in 5 min) every sessions, would EMOM be the shortest time you would keep for most regular sessions? Would I assume if you're easily able to swing quicker than that, you're probably time to move up in size?
Yes, but...
Daily S&S swings should be a hard fast effort (alactic) plus plenty of recovery (aerobic).
A 5-minute test will be less than adequate recovery for the alactic system so will likely bring in additional energy (glycolytic).
If someone does their swings in 5 minutes in daily practice and it's NOT easy, they are spending a lot of time training the glycolytic pathway. Fine for every once in a while (once a week or every 2 weeks), but not ideal for daily practice because this can be stressful and isn't the best way to meet the objectives of S&S swings. (Most people know this as it's been written about often, but bears repeating for newbies!)
If someone does their swings in 5 minutes in daily practice (or a 5-minute test) and it's REALLY easy, they are probably swinging too light of a bell. Not ideal because they are not challenging their strength, power, technique, or alactic energy pathway. So, yes, this could indicate it's time to move up in bell size.
I think S&S intends for you to move up in bell size when you can do 10 x 10 swings in 5 minutes without any loss in power and technique. IMO that will still be a fairly hard effort.
On your first question, yes, I think swings EMOM is usually about right for daily practice. If you can do a good hard set of 10 swings, and then feel fully recovered (breathing, heart rate, power restored) by the top of the next minute, it's probably a good size kettlebell. If you feel fully recovered way earlier than that, you either have VERY well-trained alactic and aerobic systems, or the load is not adequately challenging.
If you need longer than EMOM, that's fine too, as long as the swings are good.
That probably goes way beyond your question but I wrote this after 2 cups of coffee.