When Jesus says to love others as in the same way we have been loved by Him, He's not talking about the way our culture defines love. He's talking about a Biblical love based on sacrifice, dying to ourselves and laying ourselves down for our friends.

Abiding and remaining in Christ means doing what He says. This means not just saying that you're a Christian, or that you love God. But out of joy in the Lord, knowing that He has saved you from your sin, faithfully serving Him.