"The person across from you" means "the person opposite you". If it is the person straight in front of you, you could say "the person straight across from you" or "the person directly opposite you". In this case, the text conjures up the idea that you are in a room full of people that you don't know personally (like maybe in a train or bus). You should try to imagine what the stranger sitting opposite you is thinking when they look at you, which will give you a new perspective of yourself. This can help you to see your own flaws which you are perhaps blind to, and thus be able to improve yourself and achieve your goals.

I guess here "from" is surplus and it was meant to be: "the person across you", or "the person in front of you" - the person with whom you have relations.

Across from (you): It's a metaphor for the person next to you. It's a metaphor for the person in the same physical room as you are. It can be a metaphor for the person who is in a similar situation as you are. The sentence is passive because of the gerunds (ing) position to achieve your own objectives = could be written as = position to begin achieving your own objectives so that it is parallel with the rest of the sentence.