Earlier quoted context omitted.
> you can't just clam up halfway through a conversation Why?
I'm not a lawyer, but I've heard that the 5th Amendment is an "all or nothing" thing - that a judge might say you answered all these other questions, so you can't pick and choose which ones you don't want to answer, so now the court is compelling you to answer.
> If you decide to answer questions now without a lawyer present, you have the right to stop answering at any time.
If the questioning goes from "what's your name, what's your job, where do you live" to "why did you murder so-and-so", you're allowed to invoke the Fifth there, even if you answered the innocuous questions earlier.
At trial, you can't start testifying on your own defense and invoke the Fifth part way through, but you can during police interrogation. https://www.findlaw.com/criminal/criminal-rights/fifth-amend...
"Once the defendant takes the witness stand, this particular Fifth Amendment right is considered waived throughout the trial."
(Witnesses have full Fifth Amendment protections while testifying, oddly enough. The above is specific to a) trial and b) the defendant)