self-interest alone indicates that such acts where we can help people a lot with relatively little effort are moral. feeling a "genuine interpersonal connection" is not necessary but it's not immoral to feel it.
a truly self-interested person sees the benefits of living in a society. the division of labor allows humans to live a much higher quality of life. the more people there are, there more division of labor there is.
morality deals with the effect of your actions in the long term. helping one particular person once might not benefit you, but you do it because it's good practice. just like telling the truth one particular time might not benefit you, but having the practice of always telling the truth will likely benefit you in the long term (lies can sometimes be revealed in weird ways, and when it happens you lose credibility).
human relationships and friendship are perfectly OK under Objectivist Ethics. if your morality is based on Objectivism, you will naturally be attracted to people with your values: hard-work, ambition, independence, etc., and their company will not be a burden but the contemplation of their virtues alone can inspire you to accomplish more things yourself, when you're shown that over human being is dong it, even if you're an accomplished person already.
so there is no altruism at all in anything i described, and yet you can have relationships and helping people. it's morally permissible to say the least.