Electrical – Does replacing an electrical junction box require the wiring to be brought up to code

TL;DR -- find the breaker that shuts that red wire off, then slap the builder with it, so to speak

The builder of your house needs a slap with the NEC. There are two very clear Code violations here, and they're both things that are trivial to avoid.

First off, the lack of panel labeling isn't just a massive inconvenience to you, it's against Code -- the NEC requires it so that the next electrician/homeowner who looks at the panel can actually figure out what breaker to shut off to make a circuit safe or get that sparking oven to quit. In particular, it'd get dinged for busting 110.22(A):

110.22 Identification of Disconnecting Means.

(A) General. Each disconnecting means shall be legibly marked to indicate its purpose unless located and arranged so the purpose is evident. The marking shall be of sufficient durability to withstand the environment involved.

and 408.4(A)

408.4 Field Identification Required.

(A) Circuit Directory or Circuit Identification. Every circuit and circuit modification shall be legibly identified as to its clear, evident, and specific purpose or use. The identification shall include an approved degree of detail that allows each circuit to be distinguished from all others. Spare positions that contain unused overcurrent devices or switches shall be described accordingly. The identification shall be included in a circuit directory that is located on the face or inside of the panel door in the case of a panelboard and at each switch or circuit breaker in a switchboard or switchgear. No circuit shall be described in a manner that depends on transient conditions of occupancy.

Second, what you have is indeed a Multi-Wire Branch Circuit (MWBC) -- the 52V on the black wire with breaker #23 OFF is stray capacitive coupling from the still-live red wire. The red wire, of course, is still live because of another Code violation, this time of 210.4(B):

(B) Disconnecting Means. Each multiwire branch circuit shall be provided with a means that will simultaneously disconnect all ungrounded conductors at the point where the branch circuit originates.

So, it's time to find the breaker that turns off that darn red wire (leave #23 off while you do this!). Hopefully it will be adjacent to Breaker #23 -- in that case, you can get a handle-tie from the electrical supply house and handle-tie the two dodgy breakers together to fix the issue as per 240.15(B)(1). If the builder was as clueless as I fear though, that breaker is somewhere totally else in the panel -- something you'll want an electrician to fix.

Answering your questions in turn:

1. Yes, you would have to bring Circuit #2 up to Code if you altered it. The applicable provision is actually E3401.4 of the International Residential Code as your jurisdiction doesn't use the Annex H model legislation to adopt the NEC.

2. The primary hazard the current wiring poses is that tripping Bathroom 1's GFCI turns the lights out on the unsuspecting occupant of Bathroom 2, which could lead to a minor disaster (say involving a hot curling iron, or stumbling and falling in the shower in the dark).

3. Adding the fans to circuit #1 isn't a problem, by Code -- bathroom outlets other than the required receptacles serving the countertops can be on any general-use branch circuit. With a fair bit of rewiring, though, it's possible to juggle things so that the bathroom lights and non-bathroom receptacles move to circuit #1 while the bathroom receptacles stay on circuit #2, which would make things almost fully Code-compliant (bathroom #3 would need to be addressed separately, but that's simply a matter of putting a new breaker in the panel and moving bathroom #3's homerun to it, based on your diagrams).

4. Last but not least, you don't need a divider to put two different circuits in the same wallbox as the voltage between adjacent devices can't exceed 300V on a residential 240/120V service. The requirement for dividers between circuits in mains-only boxes only kicks in for commercial folks and their 277V lighting circuits, see NEC 404.8(B) for details.