Electrical – How close can I bury circuits to each other

I'd agree with Keshlam, ask the local inspector about that specifically. It sounds to me like you don't plan on taking out a permit, which I would probably recommend, it gives you peace of mind knowing the job is done right, it's not very expensive, and you can tell the future homeowner when you sell that it was inspected and done to code.

As for circuit design, you said 6 circuits could be a limitation? Then what I'd think about doing is:

• Both bathroom lights on one circuit
• Bathroom GFCI Receptacle
• Bathroom GFCI Receptacle
• Largest and Smallest bedroom Receptacles
• Two other bedroom receptacles
• All bedroom lights (Assuming they don't exceed 12 fixtures)

You probably won't want to have all the lights from one floor on one circuit, as if that circuit ever trips, you'll be in the dark with no supplementary light to guide you.

For conduit fill calculations you have to treat romex/NM as a ROUND wire of the same size as its largest dimension (ie, the long axis of the oval.) Oddly enough this means that 14-2 is larger than 14-3 for conduit fill. As @SpeedyPetey notes nipple (less than 24") fill is 60%, not 40%, and is a LOT of wire to get into a conduit; but I don't think that's the major issue here if NEC compliance is a desired upgrade. The wire type and location is the main issue.

NM cannot be run in exterior/underground conduit since it is not rated for wet locations. With an outside service box that alone might mean you can't do this and meet code - at which point you'll need a major junction box or a lot of minor junction boxes inside, and some wet-location-rated wire until you are inside.

(And now that I've seen the pictures...)

My understanding of NEC (which does not seem to have been particularly involved in your current service, with exposed NM running outside) is that you would have to run a wet-rated wire (THW, XHHW, etc.) until you get inside the house, where you would connect to the interior type wire you currently have exposed to weather and sunlight. NEC defines (and reality frequently confirms) all exterior conduit as a wet location.