Re: coming in 15 min early - were you claiming pay for this time? You supervisor may have an issue with you claiming pay before your shift actually started - they didn't agree to pay you for more than a certain number of hours a day. I bet you were, because otherwise coming in a little early shouldn't be a problem at all. Surely she must have explained why that was a problem & you are leaving something out here. Or maybe she didn't get a chance to expain because you just walked out (then you also said you don't understand why she wouldn't approve your time off - hello, you didn't let her explain because you "just walked out."
Re: time off - You should have been allowed time for your court date, and you were.
Vacation fun time is completely different. You were a fool to resign a job over that in this economy, especially a job you were "dying for." Oh well, at least you created a job for someone else who will appreciate it.
Many employers make you schedule your vacation by the end of the preceding year. At almost any job, vacation time is approved based on how many people they can allow to be off at the same time due to coverage needs, with seniority in the company given preference. This also depends on what your employer's policy is on how much vacation you get each year & how long you need to be there before you earn it. Typically you have to have been there either for a full year, or you get it in your first full calendar year. Did they not tell you their time off policies at your interview?
Given your reaction to your boss when she tried to talk to you about this, it sounds like you were doing her a favor by resigning just a month into your employment. I wouldn't want an employee like you. God knows what it would be like to deal with you if there were a real problem. You sound very immature & unprofessional.
When you find an employer that lets you take vacation any old time you want, let me know where so I can apply there too.