Any person who became a resident of New Jersey during the year and whose income from all sources for the entire year is greater than $20,000 ($10,000 if filing status is single or married/CU partner, filing separate return) must file a New Jersey resident income tax return (Form NJ-1040) and report that portion of their income received while a resident of New Jersey. Taxpayers who lives in NY but works in other states maybe eligible to claim a credit on NJ tax return for taxes paid to the other states.
Texas has no income taxes for individuals.
Conclusion:You will need to report all your income( including Texas income) on NJ tax return. No tax in Texas.
No, you don't have to. The procedure can be different state by state but there should be a way to elect out. Which state is your employer located?
If the paycheck is from Texas, Texas has a rule of withholding otherstates' taxes. They will withhold your New Jersey tax on your paycheck.
Yes, you do have to keep track of which states you have to pay taxes.