If I’m cut off by a driverwho doesn’t signal and then I’m rear-ended by someone on a cell phone, what can I expect?

You can definitely sue if  you feel the other driver--e.g. the rear driver, on the cell phone-- is at fault. You may sue for property damage, cost to repair, towing, medical costs, lost wages (if any, etc.). If you sue and win--or even if, on initially submitting a claim to the other party, his or her her insurer decides your case is so good, it will pay without making you prove you case in court--you should receive more or less full reimbursement or compensation. If the other side thinks it was not at fault--and therefore does not have to pay--contests or fights the case, and ends up winning, then you would receive no money from them.

Typically, the rear driver in a rear end collision is found to be at fault, since it's considered that he or she had the better chance to avoid the accident (e.g. follow at a greater distance). That's not to say that the rear driver is always at fault, but more often at not, he or she will be found to be. Similarly, a driver talking on the phone will driving is more likely to be found at fault than one who was not.

You also could submit a claim to your own insurer, if you have collision coverage.