You don’t have to say anything to the police. hence the NTTC advice.
If the prosecutor puts together a grand jury, then anyone who is subpoena’d has to take the stand and testify. they can (legitimately) “plead the fifth”, that is, decline to answer questions where they believe they would incriminate themselves. However, if this happens, the prosecutor can give them immunity from prosecution for those crimes, in which case they are the required to answer the questions they pleaded the fifth on.
Prosecutors (and anyone) cannot suggest to a judge or jury that your pleading the fifth or refusing to talk to the police should be taken as proof of guilt in the trial at hand.
As mentioned, failure to testify when obliged to can result in contempt of court charges.
The same situation about testimony applies at any trial. Once a matter has become a matter of criminal law, you don’t have the option (like you do with the police) to say “I’d rather not answer.”
The defendant in a trial has the option to not testify. If he does testify, however (IANAL) he cannot then plead the fifth(?). This means, a defendant can’t get up on the stand, say “I didn’t do it, I was with my late grandma watching TV” and then refuse to answer any more detail. You either testify and answer questions, or you don’t. No halfway. Once again, declining to take the stand cannot be raised as an indicator of guilt. The prosecutor cannot say “if he didn’t do it, he would have gotten on the stand and said so…”
(If you watched Law and Order UK, you would have seen an interesting exception there: “If you fail to mention something now and bring it up later, that omission may be held against you.” Should you suddenly say just before the trial “I was with me grandma all day when the murder happened” the prosecutor ***can ***point out you didn’t mention that for 6 months when first arrested. Implication - you just now made it up…)
I don’t know what the criteria are for empanelling a grand jury and compelling testimony. Generally, it seems to happen when the prosecutor knows which person or ham sandwich he’s looking to indict and wants to be sure the necessary testimony details are there. I’m not sure it’s used as a fishing expedition when they are not sure what really happened… but I may be mistaken. It’s convenient too, because it will expose any problems with testimony or the reluctance to provide it, which can be resolved before the matter gets to an actual criminal trial. Not sure (again, IANAL) but you can’t just put a trial on hold halfway through waiting for a witness to testify for months or years; and once a jury is empanelled, the defendant cannot be retried if found not guilty.
With the OP it seems the family’s lawyer is either trying to guilt the witnesses into telling what they know, or shame the prosecutor into doing more.