How do I cope with hating that I look like my dad and feeling hopeless?

how old are you. to me you are a general pink photo, so I have little context.

I was told I was ugly by some and it hurts more by family. At what age did this happen because it's development stage of a developing person and can be impactful. Either way, that be part of understanding you, why you are hurt so and how to get free from it.

I got a lot of negative from girls younger age and picked on by boys. People are mean sometimes. Not being homecoming queen... that's a tall order there, only one person can be and honestly, it doesn't mean that much, but does at the time. Time goes on, people change.
You've taken some insults and it isn't just physical but emotional. Once these unfeeling abusive people have you down, they keep going because you look like they can abuse you. Part of the issue is... they are abusive and you don't have the power yet to uphold yourself.

I know plenty of people that look mediocre, found mates, have kids, etc.. You cannot judge anything by what these other people said.

No dates, kisses , etc.. yea, I didn't have those til much later either. When you get hurt early, it delayed you.
I suggest you spend some time learning about yourself. are you a sensitive person, are you caring, are you empathetic? If so, it's easy to have hurt you, but these are really great gifts and of your value. You have to learn to love yourself, so spend time learning about love, forgiveness, hope, having faith, gratitude, etc.. Those are the salves that heal this wound. Of course, getting some better more positive people around you.

You really have to not be so critical of yourself but focus on making yourself the best person you can be, the inside and outside. Again, I've seen so many people not really that attractive find others. What's essential is you feel good about yourself, that projects and changes how others see you. The abuse you took, wrongly so, warped your view of yourself. That needs improved. You must look in that mirror, and love that person. So just do that, practice it, speak to yourself, repeat it until you believe it. Tell yourself you are beautiful, or say what is great about you, Say what you want your life to be, write it down. Focus on what you can control and do.
Avoid all the surgery if you can.
Your time is not over, you are still young. I know people married in late 40's that got married and had kids.
I know attractive people... not married or had some miserable days. Dont envy others. Be your best.

link does not work. That will cheapen you which is what they told you you are. you need to go the other direction to up your value. What's the chance you can explore going to church, get positive prayer, accept God's love, and rebuild yourself. that is what I did, that's what I recommend. Going out on the internet to bait guys will just reinforce the evil put upon you. Go the other direction.

Time to start on that relationship. You started as a tiny cell... you got a lot of something to get to where you are. Many others, not so fortunate. Write down a few things you can be thankful for.

I re-read parts about your mom and dad. There's family patterns of issues and abuse in here. There's a state of life as a teen where these form your identity. That is what you are battling with. You have self image issue.
This has nothing to do with other men but how you see yourself, which is flawed, but it's the reference point you were given.
So you must go find a new perspective on life, on yourself.

I had to do that as do others. When you get to the point of freedom, it will be a wonderful feeling.