Applying for multiple credit accounts can often damage your credit score more than simply applying for one credit account. The fewer accounts that you apply for the less damage will be done to your credit score.
Be sure to research the features and terms of each card that you are interested in, and then apply only for the credit card that offers the best features.
Your credit score presents a fairly accurate picture of your credit history, but not every account is recorded. Certain things like your good history of rental and utilities payments are not listed on your credit report. Positive information from your landlord, cable, and cell phone providers is not reported to the credit bureaus.
No, in general credit scores do not change that much over time.
There are a variety of factors that impact changes to your credit score over time, such as: