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It means that whatever the subject of the motion or writ was, it was reviewed by the judge and he denied it.
The case moves on
It may depend on the context, but in general it means that the motion no longer has any value so it was denied simply because it doesn't matter. For example, suppose you file two separate motions: one to dismiss a case against you, and another to exclude certain evidence so it can't be used against you at trial. If the judge grants your first motion, then the second is meaningless; no evidence will be used against you because there will be no trial. Therefore, the second motion would be denied as moot.
It may depend on the context, but in general it means that the motion no longer has any value so it was denied simply because it doesn't matter. For example, suppose you file two separate motions: one to dismiss a case against you, and another to exclude certain evidence so it can't be used against you at trial. If the judge grants your first motion, then the second is meaningless; no evidence will be used against you because there will be no trial. Therefore, the second motion would be denied as moot.
A motion by a debtor to dismiss a case under Section 1307 B means that any debt not settled under Chapter 7 bankruptcy, can be dismissed. But, this is only under certain conditions.
this means that the petitioner has been denied free counsel, and must seek their own, or prove that they qualify for said counsel.
It means that someone (probably the losing party) petitioned the court to have the case re-opened and the original judgment re-considered. A hearing on the matter was conducted by the judge - and after hearing arguments for and against, the motion was DENIED.
More info required from questioner - what do you mean by "dismiss" a criminal record.
When someone brings a suit against another person or entity, they can file a Notice of Non-Suit. That is, they can dismiss their own case. A Notice of Non-Suit says that the plaintiff prefers not to pursue the cause any further. An order granting the plantiffs motion for nonsuit is signed by the judge saying that the judge received the order of Nonsuit and will dismiss the case without prejudice.
It sounds like stealing to me.
Dismiss
No, it is not. Dismiss is a verb, which can mean release (a class, a subordinate) or ignore (a threat, a court case), or terminate, fire (an employee).