Any time I do or think anything apart from the will of God, I sin.
"What is the measure against which you recognize your sins?"
I believe Jesus established a rather high standard in the Sermon on the Mount. It is not only what I do (or what I fail to do) that I must examine when I look for sin in my life, it is my intention -- am I motivated in all that I do and think by God, or am I attempting to be in control?
"Are all sins forgivable?"
I believe the only sin that Christ identifies as being unforgiveable is the "grieving of the Holy Spirit".
"More importantly, once you believe you have sinned and ask forgiveness from God, how do you know it has been granted?"
Because I take God at His word. IJohn 1:9: "If we confess our sins, he is faithful and just and will forgive us from all unrighteousness". I believe that promise of God.
Not to seem like I’m piling on, but your quote of 1John 1:9 is a good passage to harmonize with the Our Father as well. Notice that “asking,” as in the Our Father, and “confessing,” as in this passage, are not necessarily the same thing, as people would ordinarily understand them. Yet, you yourself equate the “confessing” with “asking,” or at least you seem to make them synonymous. So, in fact, you are not too far off from being able to see that God has tied into His plan for us the notion that He will dispense His forgiveness through “confession.” And confession is through another mere man, namely, a priest with the power to do this transmitted down from the Apostles, who received it from Christ Himself. To God be the glory!