You have asked some good questions.
I think that loving God with all my heart means joyfully allowing him access to all of me, body, soul, and spirit, and all of my time, possessions, abilities, finances, and anything else I might have, and desiring to give myself to Him.
I know how it feels to not be sure God exists. I went through a period of my life like that. Somehow, though, I must have believed, because my heart cried out for the ability to believe, and I now understand that I was crying out to God. I think there is something in the core of all of us that believes, no matter how much we might want to have proof or think it's lame to believe without it.
just my thoughts......
blessings
tal