Wanting a partner is completely natural and not something to be ashamed of. Thinking that it will constitute 70% of your happiness as a young man is crazy. Most people don't want to admit this, but one of the only things a partner can give you that you can't readily get from other areas of your life - is sex. I enjoy sex as much as the next guy, but my life was pretty fucking awesome for a really long time before I got my first long-term girlfriend and was fucking regularly. It was honestly a lot better while I was single because I was still physically healthy. My life was awesome and full of great shit and that was a very attractive quality.
Something you notice is that paradoxically, the less you need other people, the easier it is to bring other people into your life. Finding a partner would make you happier but honestly, improving the life you have currently and just getting laid occasionally would lead to a much better life than whatever the fuck you think you want right now.
As far as bars and parties go, invite your friends to go with you and go out as a group so it's less intimidating. If it seems like your friends don't want to go, then try to be the guy that's social and gets them out of the house. And yes, it is actually pretty normal to just go up and talk to people in groups at bars. People go to those places as a way to meet new people. It takes a lot of practice, and it's gonna be awkward at first- but you'll get better at it (don't be afraid to drink a beer or two- it can really help.)
Yes, the majority of women want guys that are tall and attractive. They would also like these men to be immensely powerful, extremely wealthy, wickedly intelligent, and also very sensitive. The majority of men would like their women to be irresistible attractive, have incredible bodies, be extremely friendly, and go along with whatever they want. We all have a very high ideals for the type of partners we would like, but when we find someone that we connect with in real life - these standards kind of get thrown out the window. You've been in a relationship before so you know that you start to find someone's faults endearing. The Internet is very bad for your self-esteem and is honestly not very representative of how successful people can be in real life. I hate to be an anecdote guy but I've known plenty of dudes that were not very tall and not particularly good looking that got laid constantly because they were confident, fun, and just had a lot of practice being social. Life is easier for attractive people but it's also a lot easier for smart people. Utilize the fact that you're a smart person to learn how to live life like a confident, fun person.
Start lifting weights ASAP. Getting even slightly muscular will do wonders for your anxiety and will make you a lot more attractive.