Yes, you should be able to login to your account to see stats. There is usually a delay in the reporting data, but after a few hours, you should be able to see the number of impressions.
If you are using broad match, or phrase match keywords, you will not know in advance which keywords will trigger your ads. Depending on the ad platform, you will usually find a report that can be generated to show which keywords triggered your ad.
This link will help you understand which keywords might trigger ads for the different match types: Using keyword matching options – AdWords Help
If you are using Google AdWords you will be able to generate a Search terms report to see some of the keywords that are triggering your ads (It only shows keywords that generated clicks).