Okey Dokey!
First of all, since they are of type Dragon, do they get Darkvision 60' and Low-light vision like other dragons? (MM 308)
Yup, you get Darkvision and Low-light Vision. Spiffy, no?
Do they get natural armour? In humanoid or dragon-oid form?
Nope, unfortunately, the Mojiin's scales have grown soft due to the weakening of Arris's life-force. You can always turn into an animal to get some natural armour, and there's a feat that lets you spend a Wild Shape attempt and gain a bit for 10 minutes.
What happens to my equipment when a Mojiin change shape? Does it get absorbed into the new form, mutate to fit the new form, or simply break/fall to the ground?
It either shifts to fit your new form or gets absorbed if it cannot (like weapons or non-Wild armour).
Also, what are their stat modifiers when they go into their dragon form? Also what is their Size, Movement rate ...
Stat modifiers remain unchanged, as does Size and Movement rate (except the flying rate, as noted, if they have wings). Mojiin are Medium-sized dragons that can turn into a humanoid form, but the dragon form is their true form.
What color are the Mojiin's scales? Do they depend upon the breath weapon? If so, can they be chromatic or metallic (ie red, brass or gold for fire)?
Mojiin scales have varying colours, as noted, although the colours generally correspond to breath weapons, they do not always, and there are also colours that are not a colour of any typical dragon (like a lavender colour that many Mojiin find to be rather beautiful, like some humans think of blondes).
What is the DC for the Breath Weapon?
10 + 1/2 HD + Con mod, like every breath weapon.
Can I take the Multiattack feat (MM 304)?
Yup and its an awesome choice if you plan on using natural attacks in Dragon or Animal form. You may also want to look into Improved Natural Attack (Claw)
If I attack with a weapon as well as a claw and a bite, is the claw considered a secondary attack, or do the rules for Two-Weapon Fighting take effect?
The claw is normally a secondary attack. However, you can also treat it as a second weapon and make iterative attacks if you have the proper feats (Rapidstrike and Improved Rapidstrike from the Draconomicon, which can only be taken by dragons and a few other things and give multiple claw attacks).
Do they have the same weapon and armor restrictions as Druids?
Do they get a d10 hit points per level?
Do they get the starting weapon and armor proficiencies of both Druid and Paladin?
All exactly correct.