During the general confession (non-private), do I have to bring/mention my sins mentally before God for Him to forgive them? The liturgy moves too fast and I don't have time to silently bring my sins before God. Does that matter, or are all my sins forgiven anyway?
As opposed to private confession when we might confess specific sins, the general confession in our worship services provides the opportunity to confess our sinfulness (our sinful nature) and our sins of thought, word and deed (both sins of commission and sins of omission). You are correct in observing that the pace of the liturgy does not allow for enumeration of our sins.
You and I also recognize that we cannot list all our sins before God. We may not even be aware of some of the wrong things we do and the good things we fail to do (Psalm 19:12).
Certainly, you can use the quiet time before the worship service begins to confess specific sins to God. There are helpful resources in our hymnal to assist you with that.
The wonderful news about the confession of sins is the promise that God gives in his word: “If we confess our sins, he [God] is faithful and just and will forgive us our sins and purify us from all unrighteousness” (1 John 1:9). Remember that, and keep in mind that we stand in grace before God (Romans 5:2).