Handling errors: If you make a mistake in your logbook (and you will at some point), simply draw one line through the mistake so it is clear to the reader what adjustment was made. No scribbling. No white-out.
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61.59: “Falsification, reproduction, or alteration of applications, certificates, logbooks, reports, or records.” In a nutshell, no person can make or cause to be made a fraudulent or intentionally false logbook entry, and violations can lead to suspension or revocation of an airman certificate, rating or authorization ...
Date. Total flight time or lesson time. Location where the aircraft departed and arrived, or for lessons in a flight simulator or flight training device, the location where the lesson occurred. Type and identification of aircraft, flight simulator, flight training device, or aviation training device, as appropriate.
Short answer: an electronic logbook is legal; the FAA will accept almost anything as an endorsement; it's often most practical to collect endorsements on paper but electronic versions are also fine.