1. Does loving God help me obey Him or does obeying God help me love Him?
2. Is this important?
3. Why or why not?
4. Why is love greater than faith?
1. I say neither. As many of the passages you included demonstrate, loving God is submitting to His perfect will, which we find revealed in the written Word and exemplified in the life of the Lord Christ. To love God is to obey and obeying is demonstrative of love. Perhaps one of the greatest expressions of this truth is the whole of Ps. 119. Notice how this Psalm of love for God begins:
Psalms 119:1-3 (ASV) 1 {aALEPH} Blessed are they that are perfect in the way, Who walk in the law of Jehovah. 2 Blessed are they that keep his testimonies, That seek him with the whole heart. 3 Yea, they do no unrighteousness; They walk in his ways.
"Blessed" here and in so many other places in Scripture is not to be translated nor understood as 'happy', but rather 'to be in God's favor'. We love Him because He first loved us (1Jh 4:19).
2. Loving God in obeying Him is ultimately important if for no other reason than it justifies our confession (Jam 2:24). Our loving obedience reveals that we are loved of God for it is God dwelling within us by His Spirit to work and to will for His good pleasure (Phil 2:13). It is the foundational expression of our love for God that we keep His commandments (1Jh 4:20; 5:2; cp. Jh 21:15-17).
3. See #2
4. Re: 1Cor 13:13... What Paul says regarding our love while we are in this earthly state may surely be used to cast a light upon our state above where it will be love that brings us into the fullest union and communion with God. It is faith's nature to receive, but love gives; and giving is greater than receiving. God's fullest purpose is attained in us when we are filled with love. Hope also looks forward to receiving, but love is full possession and completed joy. And for every new joy which hope receives in heaven love will be the response on our part. When we come to rest on the bosom of God, it will be by love.