Can Lawyers Impeach Jurors During Voir Dire?

Assume these scenarios:

During voir dire counsel for both sides are searching juror's names on social media sites such as Facebook, as well as "Googling" their names, for information about  jurors.  Assume these various scenarios.

One of the attorneys discovers a prospective juror:

1.  Has a felony record (uncertain if rights have been restored) which was not disclosed (and falsely so) during general voir dire by the judge

2.  Has been commenting in general about jury selection and the type of case on his/ her  Facebook page

3. Failed to disclose that he or she had been employed in the industry of which one of the parties is involved and was:

    a.   A clerical employee
    b.   In a technical or research capacity as an employee
    c.   A "whistleblower" to the government for which they were highly compensated

4.  Is a member of an organization which might make them biased, eg.  a member of MADD for a DWI trial

My questions would be:

1.  If , as an attorney, you decide to seek a juror's dismissal, do you move the court out of the hearing of the jury panel?

2.  Do you request permission to, basically, impeach the juror, giving them the opportunity to explain?  Out of the hearing of the other jurors?

3.  As a judge, how would you handle these scenarios?

4.  As a judge, do you warn the jurors that lawyers may be looking at their Facebook pages?  (I wouldn't.)

These are all questions worthy of discussion
 and thought.