Where do I need to fix grammar? I know for a fact something must be wrong...
于一文: 你好! 祝你生日快乐!!! 对不起, 让你久等了。祝你年年有今日，岁岁有今朝。祝万事如意。谢谢你的万事。有机会的话，大家见个面。
If 于一文 is your friend, you should just use the first name 一文, and write: "一文, 你好!"
If you like to keep English favor in your letter, you can add 'dear' like in English letter and write: "亲爱的一文, 你好!"
祝你生日快乐!!! 对不起, 让你久等了。
If you need to apologize for lateness, better put it in first, and write "对不起, 让你久等了, 祝你生日快乐!!!"
This phrase is kind of dated, and only suitable for blessing a person in advanced age or at least in late middle age. If you must use it, put it in a separate paragraph to emphasize your blessing
No problem with this phrase
It is an attempt to translate "thanks for everything" but we don't use 万事 this way (the correct usage is another topic). The literal translation is "一切都多得你" ; However, "thanks for everything" imply "thanks for everything you have done for me" which shouldn't be omitted in Chinese, so the correct translation is "谢谢你为我所做的一切"
It sounds like you and this person rarely have chance to meet. If it is not the case, you should add "next time" and write: "下次有机会的话，"
It sounds too blunt, I suggest "(希望)大家(能再)见面。"
Do you mean: "你不但是我的老师, 也是我的哥哥。"?
Chinese don't use to say "I love you" but you are not Chinese, so it is ok.
Here is my edition:
对不起, 让你久等了, 祝你生日快乐, 万事如意!!!
谢谢你为我所做的一切! 下次有机会的话， 希望大家能再见面。
In Chinese, we only use 万事 at the beginning of a phrase. It acts like an exclamation.
"万事有我" (I would deal with everything!)
"万事都有例外" (There's exception in everything!)
见个面 (meet once) --> 能再见面 (can see each other again)
I would say 兄长 is better than 哥哥。
Consider replacing '哥哥' with '兄长' and write: "你不但是我的老师, 也是我的兄长" if you want to be more formal.
However, using '哥哥' is also acceptable, and it shows more passion-- consider the next phrase is "我爱你"