Q. Can dependent have their car which is titled in their name registered, insured and titled at their college address and still be a dependent for tax purposes?
A. As the other answer already said, car ownership, registration and insurance ain't got nothing to do with income tax filing and dependency.
Q. So even if your dependent's car is insured and registered in a different state then parents, the dependents' taxes would be filed in the same state as parents, and then they just file non resident to the state where they had earned income (where they went to college)?
Q. Residency is determined by parents address and not by car registration or insurance or where the kid goes to school or earns money?
A. Simple answer: yes. If he/she qualifies as the parent's "qualifying child"* dependent, then the parent's address is his address and his residence for tax purposes.
So, yes the student may still have to file a non resident income tax form for any state he earns money in; but that is in addition to the resident income tax form he files for his (and the parent's) resident state. The resident state usually allows a credit for any tax paid to a non resident state. But, it also depends on what states are involved; reciprocal state rules my apply.
* There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test. The support test, for a QC, is only that the child didn't provide more than half his own support. The support test for a Qualifying Relative is that the taxpayer provided more than half the relative's support.
