Your first question is answered here:
LORE: Restricted MulticlassingSo taking a level in Barbarian after a Druid/Shifter path would mean the Druid can no longer call upon his/her druidic powers until the druid returns to the path through a CDQ.
Also, keep in mind that a Barbarian/Druid is still limited to the weapons and armor of a Druid. The character is essentially a Druid with some barbarian in his/her past. Becoming a Druid is a lifestyle change, with all the benefits and burdens that come with it.
A
Shifter is a druid who does not base his/her identity on physical appearance. It is not that they are more in touch with their animal natures but rather have come to realize a separation of form from identity, and take whatever form is most beneficial or expedient at any given moment. Given that many Shifter forms are not even animals further illustrates that it is not about an "animal side."
Nature is everything to a druid. Some druids are people of faith as well, but they are druids first and foremost. Their service is to Nature. Their strength comes from Nature, but it is not necessarily true that they see Nature as a Divine Entity.