1. I sort of understand the doctrine of Unconditional Election, but I am wondering, how do I know if I am predestined to salvation?
As others have pointed out, you know you are saved by your reliance (== your faith) in Jesus Christ. Predestination is the process, it is not the condition of salvation.
You're certainly furthered in your
assurance of your salvation by what you do. You become aware that you know accurately this Jesus you depend on, because you find you're doing what Jesus commands. (cf 1 Jn 2:3). However, this awareness doesn't save you. Faith alone saves. Given time and opportunity faith indeed issues in submission to Jesus' commands, working the works of God. "Faith alone saves. The faith that saves is not alone."
Also, doesn't it seem futile to evangelize if some people are destined to Hell anyways?
Not in the slightest. Think of it this way: "Doesn't it seem futile to walk around thinking and acting the way your family thinks and has trained you, and discovering fellow members of your thereby, since other people aren't in your family, anyways? And what if your family actually offers the best any world has to offer -- what if your Father is actually the axis around which the whole universe spins?"
What we're doing is following the Spirit of God, because we're born of the Spirit of God. We're spiritual because He's spiritual. We proclaim His kingship, because it's the truth. Finding and helping and redeeming other sons of God is what we do in following the Spirit. We're part of the rescue. We're carriers of the Father's family robes, His family ring, rushing to the side of those God has rushed ahead to welcome home.
It's so critical a task, to help communicate the Father's love and dedication to His child, it's tough to understand why it would be considered futile.
2. On what basis are people destined to Hell?
They are predestined to Hell because they can't satisfy the righteous requirements of the Law. And note: everyone has this same destiny. Dual predestination condemns all to one horrific destiny, based on our own works; and yet saves some on a
different basis: the works of Christ.
Since it is not a matter of virtue, merit, or faith, why would anyone be unconditionally elected to eternal damnation?
I'm sorry, this is a mistake. The criteria are indeed a matter of virtue, merit, and faith: they're a matter of the
lack of virtue, merit, or faith -- the absence of all of which constitutes an offense against the God of the universe, and eternal condemnation. This is exactly why people are condemned to Hell.