No,Google will never ban you unless you violate the TOS. i encourage to see stats frequently so that you know how well your ads placed.Frequent checking your control panel show your interest to go ahead with google adsense.
of course not it's normal behavior for us to regularly check our account specially when earning increase by the day wheheheh right?
Not you wont be banned for logging. Infact keep logged in whole day. Also some people say logging from different PC's or different IP's is risky. Which again is not correct.