Yes, you can use Unarmoured Defense in nonhuman form, and yes, you get an additional +1 AC on top of it.
The lycanthrope PC box lists a bunch of things that you gain; it's very different to Wild Shape, where the new form replaces almost everything about you.
A character who becomes a lycanthrope retains his or her statistics except as specified by the lycanthrope type. The character gains the lycanthrope's speeds in nonhuman form, damage immunities, traits, and actions that don't involve equipment. The character can't speak while in animal form.
So becoming a lycanthrope doesn't prevent the character from using any of their class features, including Unarmoured Defense. Now for the shapeshift ability, where you've already found the key line.
Its statistics, other than its size and AC, are the same in each form.
All that this is saying is that changing form doesn't change anything about you except size and AC. The size change is straightforward, obviously, but the exception for AC doesn't make much sense. That is, until we know that the werebear gains a bonus to its AC while in some of its forms. If shapeshift didn't make an exception for AC, you'd have this weird situation where the werebear was meant to gain +1 AC but at the same time wasn't allowed. So this line of text isn't forcing you to use the default AC of a werebear, it's just allowing for the possibility that changing form might change your AC.
It should be pointed out at this point that the werebear statblock is a default stablock for an NPC werebear. The sidebar on player lycanthrope is very specific about what changes are made to your character, and it doesn't say anything about using the AC from the NPC statblock. Note also that the AC of the werebear statblock (indeed, all the lycanthrope statblocks) is just 10 + Dex mod (+1 in nonhuman form).
So yes, you can use Unarmoured Defense in lycanthrope form. Unarmoured Defense says that it doesn't work if you wear armour, but turning into an animal is not the same thing as wearing armour.
Finally, the natural armour bonus. This is a bonus, so it can work on top of an AC calculation; it's not an alternative AC calculation that won't stack. You might be concerned that it's a "natural armour" bonus and would therefore invalidate Unarmoured Defense, but as above, Unarmoured Defense only says that it doesn't work if you wear armour, which having a "natural armour" bonus is not the same as.