Yes, a single good GND plane is the first thing to aim for. Your circuit (especially something as simple as this) will still work without it, but it will perform a lot worse in the EMC department
Nope, the length of the power tracks does not matter much You do want fairly wide tracks to reduce the voltage drop because of track resistance. Placing proper decoupling capacitors at the “end” of such tracks (or better, near IC’s) is important though. but for this board I assume the AMS1115 PCB already has the decoupling capacitors onboard. (You should not assume, but verify).
I believe those JST connectors have a bit of a different pitch, which is troublesome for breadboards, but if you design the PCB yourself, that is not relevant anymore. You can go different roads from there. You can try to make something universal, so it does not matter on which “channel” you put a sensor. Examples are the “UEXT” from Olimex and the “Grove” from SeeedStudio. Or you can go the other way and design your project on purpose in such a way that connectors can not be put in the wrong socked accidentally. (for example by using different pin counts). Having both power and signals on the same connector is an advantage either way. It reduces cabling, and improves signal integrity and reduces EMI.
Also, very likely you can put your SMT resistors under the ADS1115 PCB. Just because there is a breakout board on top of your PCB does not mean you can’t use that area for other footprints.
This is quite enough for a starter projects. Once your PCB’s become more complicated (and have faster signals) demands on the PCB also become a bit more complex. Over time you should educate yourself about signal integrity and EMC and how that translates to PCB design.