Can a judge grant community supervision to a defendant charged with conspiracy to commit capital murder? The defendant wants to plead to shock probation. Can the judge grant probation for a conspiracy or attempted 3g offense?

Yes, defendant is eligible, assuming a sentence of 10 years or less and no deadly weapon finding. See page 69 of The Perfect Plea and footnote 30.

What if the indictment alleges conspiracy to commit capital murder by doing an act in furtherance of robbing a convenient store and killing the clerks using a firearm? Since there is a DW in the indictment, would the defendant still be eligible to get shock probation from the judge?

If the jury makes an affirmative DW finding, then the judge could not grant probation -- shock or regular.