This is related to what is known as separately derived systems and non separately derived systems, and it concerns avoiding unnecessary impedance on the grounding system that would adversely effect over current protection, i.e., breakers and fuses.
If the neutral is switched along with the phase conductors in the transfer switch, you have a separately derived system and you would NOT separate the grounds and neutrals in the generator only, which contains the main over current device "main breaker". You WOULD separate the grounds and neutrals in the sub-panel. Again, this is because the main over current device, "main breaker" is contained outside in the generator.
So, in your condition the generator is portable and thus does not fall under the permanently installed generator rules. But if it were, you would want to separate the grounds and neutrals at the generator and sub panel and be done with it.
To address your main question whether your current setup is safe. As mentioned above you ideally want the lowest impedance for ground fault protection. But by not separating the grounds and neutrals in the sub panel you are creating MORE impedance.
That is an old "rule of six" panel, which while grandfathered, is illegal under its grandfathering becuse it has 7 main breakers. Going to five is a good plan.
It is a classic "CH" panel which is a very good industrial grade panel, except that the 3/4" breaker width make non-ordinary breakers very expensive (a trait it shares with Square D QO). That makes it perfect for what you plan.
On your subpanel which would be near this panel, I would get a panel with a main breaker, with an eye toward (at some point in the future) cutting it over to be the main panel. In a subpanel, the "main breaker" is nothing more than an on/off switch, it is OK for it to be larger than the feeding breaker.
I would also get a rather large panel, at the very least 42 space and even 60 or 84 if practicable: because panel spaces are dirt cheap and often even come with free breakers, whereas running out of space is painfully expensive.
I would aim for an industrial grade panel of good repute (one available in 3-phase variants, not Homeline, BR, or second tier brands) and avoid the expensive 3/4" breakers (not CH or QO).
Over time, as you find it convenient, i'd migrate all your 1-pole and smaller 2-pole circuits over to the new panel.
For your garage panel anything would do, but I'd go for the same type as your indoor panel, so you can use some of those bonus breakers. Again it's false economy to scrimp on spaces, I'd go 20-30 at least.
Also, since garage spaces need to be on GFCI, consider getting a subpanel which has a "main breaker" which is GFCI, that way all the breakers in that panel would be protected (at the cost of potential nuisance trips, a big deal if you keep a freezer in the garage).
Ed Beal raises some very good concerns about overall capacity. One problem with these "rule of six" panels is there is literally no main breaker to stop you from drawing more than 150A. So it pays to be conservative.
It's a difficult situation because you have two big loads that operate sporadically - the EV charger and the range. And the A/C as a wildcard.
One thing I might suggest, is feed the garage subpanel from the new primary subpanel. And then move everything but the range over to the new subpanel. At that point the only things still in the CH panel would be a 60A range breaker and a 100A subpanel breaker. Even at max, those two could not overload the 150A service (by enough to matter). This would force your entire house (from A/C to EV charger) to share 100A, but would remove the possibility of an overload. This would also save you the $85 you'll spend on a second 100A CH breaker.
Best Answer
The accepted practice in most of the USA is to number the breaker slots. We number them odd on the left and even on the right from top to bottom. A two-pole breaker takes up two slots and therefore two numbers.
Some newer panel numbers are imprinted in the metal with this numbering scheme. Most construction blueprints also use this numbering scheme.
You can use whatever scheme you want this is just the common practice. The National Electrical Code requires that you complete a panel registry with descriptions of the circuits. As long as it is legible and logical, any subsequent homeowner or electrician should be able to follow it.
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