Acid catalysed dehydration of alcohol with a bicyclo group Pathway 1: Rate determining step is the formation of carbocation. In this pathway, a conjugated tertiary carbocation is generated as an intermediate.

Pathway 2: One of the resonance form of intermediate carbocation proceeds to produce a more stable  product (due to benzene ring) through alkyl migration. Though, the resonating form of carbocation is conjugated secondary carbocation which is less stable than the carbocation formed through pathway 1.

My questions are:
1- Is tert-butyl (don't know the correct term) migration possible in pathway- 2?
2- What are the major and minor products? Which factor will decide the major product: stability of final compound or the most stable intermediate?
Pathway 2 is unlikely. The tert-butyl group stays put, i.e., it remains attached to the same carbon throughout the reaction. It is the rest of the molecule that rearranges. The mechanism of this reaction was demonstrated 70 years ago. Compare this reaction with Possible nonclassical ion from a bicyclic system on ChemSE. There is information at the link on labeling to elaborate the mechanism.