#1. In what sense are strangers worthy of my love and in what sense am I worthy of the love of a stranger?
They, and you, are creations of God. Beautifully intricate little miracles, made in His image and likeness. Christ tells us that whatever we do to one of these people, that thing has been done to Him. You often hear "treat others as you would like to be treated", but what He tells us is to treat others as we would treat Him.
#2. To love all people would basically make it so that you don't have any enemies at all. Your enemy may hate you from his perspective and be your enemy, but from your perspective you have no enemies. How will that not take passion out of life? There's passion in hate just as there's passion in love.
There are ways of using our sensual abilities which bring us closer to God, and ways which turn us farther away from Him. We were created to participate in the former way, and that is where we find lasting contentment and fulfillment. The latter is a cheap knock-off, a misuse of our capabilities. The correct use of the passions fills us, the incorrect devours us. This is true not only with feelings like love and hate, but of all things pertaining to the human life. Think of food - if we eat nutritious things in moderate amounts we are healthy and satisfied, but if we eat only junk foods and either too much or not enough, we are unhealthy, obese or frail, prone to myriad illnesses. If we eat items we ought not to eat, things like rocks, plastics, chemicals, we will perish.
Though our human abilities are such that we can find a multitude of ways to use them, some ways are good for us and others are not. That we gain a new sensation from using them in a new way does not automatically mean we ought to seek this out for the sake of having that sensation. We do not (generally) seek out the sensation of being poisoned, contracting painful and deadly viruses, serious bodily injury, depression, grief, shame, embarrassment, etc. just because these things are available to us... The absence of these things, or the opposite of them, is generally thought to be preferable. So why ought we seek hatred just for the experience, when there is a joyful and fulfilling alternative?
#3. Imagine someone who has no strong feelings. He may feel in some sense strongly when he reads books on philosophy or poetry or when he engages someone in passionate rhetoric, but he feels no strong ties of emotional connection with anyone. How can such a person love in any meaningful or Christian way?
I imagine this sensation is not uncommon, though there are various degrees. For some, they feel strong connections only with those few people closest to them. For others, the feeling are only for themselves. For others, the emotional connections are with animals rather than people. For perhaps many, the connections are to things; a job, a hobby, wealth, an ideology, etc. Where your treasure is, there your heart will be. Whatever or whoever it is that you value above all else, that you strive towards, that you sacrifice for, that is where you will have these connections.
I would say that for the vast majority of people, this connection is not with God, or with all of humanity, or with even most of humanity. Perhaps there are rare souls who love as they ought to, but for most of us it is something we need to practice and try to learn how to do. A good starting point is to make an effort to pray for other people, to desire good things for them, to have a good mental disposition towards them. And then, we return to point #1... Trying to see Christ in them, and trying to do for them as we would if Christ Himself were standing before us. If we can learn to see people this way, or if we even simply wish that we could see them this way, I think God will help us in this struggle.