No, the two are unrelated. You set your budget, which is the total amount you will spend in a day. You can also set your maximum cost-per-click (CPC) which determines the amount of money you could pay each time someone clicks your ad. So if you increase your CPC you may get fewer clicks as you will pay more for each click and so use up your daily budget faster.
Google Analytics is a free, powerful web analytics tool, but do you need it? Are there any alternatives? What implications are there for privacy?