Is it possible to have seizures without EEG changes?

Yes. Having seizures without eeg changes is possible because the eeg is only going to capture a seizure about 1/3 of the time. If the seizure focus is deep within the brain it is even harder to detect. Sometimes we will do ambulatory eeg recordings to capture sleep which can increase the yield. Otherwise to capture a seizure may require video monitoring in a hospital setting. I hope this helps.
Yes and no... An eeg will usually only 'change' if you happen to catch a seizure in the moment. This is why an eeg usually involves inducing a seizure with flashing lights, caffeine, etc. Sometimes your physician may admit you for an eeg in an epilepsy monitoring unit (usually a few days) to try and catch a seizure. This may also involve video eeg to correctly localize and classify seizure activity.
YES. An eeg may or may not pick up seizure activity at the time of recording. Yield may be higher with 24 hr ambulatory eeg, but even so, a lot of activity may still be missed, as scalp recordings may not demonstrate pathology that can be shown by direct recording over brain itself. So, in some cases, diagnosis of epilepsy is based on history of spells, and descriptions of observers.
Possible. If you're not having a seizure, a eeg is commonly normal. During a seizure, most people have abnormal eegs but there are rare seizures that don't cause any changes on the eeg.