What state tax to file? Live in Texas, work for California company, and travel for work to CA and other states

Hi, I will be moving to Texas but continue to work for same company in California.  I will travel back to California for work and also visit customers in other states.  Questions:

1) Do I file Texas or CA state income tax return?  I have to live in Texas for 6-months before becoming a Texas residence.

2) Is my home office in TX tax-deductible since company has no office in Texas?

3) If work travel expenses not reimbursed by company, can I deduct them for tax?