The language of the time tended to be a little Yoda-like in its grammar, so you have to be patient with it. Also, all three of your lines run together to explain one thing: That Victor loved someone, and lost her, and now feels empty and alone without her.
1. “And expressed my conviction that a man could boast of little happiness, who did not enjoy this blessing.”
"A man [i.e., a person] who did not have this blessing couldn't boast about being happy, because if he didn't have this blessing, he could not possibly be happy."
You need the rest of the sentence to clarify the next one:
2. “I agree with you," replied the stranger; "we are unfashioned creatures, but half made up, if one wiser, better, dearer than ourselves — such a friend ought to be — do not lend his aid to perfectionate our weak and faulty natures.”
"Friend" here means lover, beloved, spouse, not "buddy."
"We, meaning people in general, are made as only half of a whole."
From here this is a complicated hypothetical, so I'm going to put the sentence back in if-then order:
You will remain only half a person if your other half isn't willing to improve your weaknesses and faults. Your other half is a person who you think is smarter and better than you, that person you love more than yourself, which is ideally how you should think of your other half.
The original, sans flourishes, runs "we remain half-creatures if the one you love does not complete you." It's the do not rather than does not which is really throwing you, I think.
3. “I spoke of my desire of finding a friend—of my thirst for a more intimate sympathy with a fellow mind than had ever fallen to my lot”
I talked about how I wanted someone to love — how I wanted a closer, deeper relationship with another person. I have never had such a close relationship so far in my life.
Here's the whole relevant passage, in order:
The tale was quickly told, but it awakened various trains of reflection. I spoke of my desire of finding a friend, of my thirst for a more intimate sympathy with a fellow mind than had ever fallen to my lot, and expressed my conviction that a man could boast of little happiness who did not enjoy this blessing."I agree with you," replied the stranger;"we are unfashioned creatures, but half made up, if one wiser, better, dearer than ourselves — such a friend ought to be — do not lend his aid to perfectionate our weak and faulty natures. I once had a friend, the most noble of human creatures, and am entitled, therefore, to judge respecting friendship. You have hope, and the world before you, and have no cause for despair. But I — I have lost everything and cannot begin life anew."