As for how we can know God loves us, that's something I think we individually have to see and feel and experience for ourselves.
In my own case, I can point to specific times when I truly feel like God has reached into my life and made themselves manifest - understanding that my choice of words to describe those experiences is slanted from the descriptions of my upbringing. There are certain things I've experienced that I simply can't ascribe to anything other than God - or, more generically, the divine outside mortal understanding. Those experiences have not been ones where I was slapped around indifferently, so I interpret them as evidence of God's love.
How do I justify that or explain it when others are sold into slavery and prostitution as children - or suffer greatly and die of AIDS through no fault of their own - or are abused throughout their lives by someone close to them - or are raised in any environment of terror and/or deprivation? I really can't - because I understand both experiences intellectually and have no idea, ultimately, why mine are mine and others' are others'.
I don't know - so I am left with the classic definition of faith - the substance of things hoped for, the evidence of things not seen.