Question: Why does Lori tell Daryl that Rick will show him where his brother is but then 10 minutes later tried to talk Rick out of going?
Answer: It's not shown, but I think Lori is suffering from some sort of PTSD due to thinking her husband had died, having an affair with Shane and of course the zombie apocalypse as well! This isn't the only time she contradicts herself so it kinda backs this theory up.
Question: When the Linden County units are chasing the bank robbers, and the car crashes, why does Rick leave the safety of cover to approach the car? Why can't they just order all suspects out of the car via the PA system on one of the cars? The bank robbers are armed and dangerous, and Rick should remember that they are most likely going to come out heavy - despite being injured in the crash.
Answer: The car had just crashed, and there was no movement. There was no way to know whether the suspects were alive or dead.
Answer: No, she actually tries to talk Rick out of it, but he's already made up his mind, minutes later when Daryl asks him about the location of his brother Lori says "he'll show you."