To remove a pic from the gallery, long press on it and there should be a delete option. If there is not, then the photo is on your Google+ account or Picasa. Log in using a proper computer and delete the albums containing those photos.
To add pics, well, Gallery just scans the internal (and on some devices external storage) and looks for any pictures and video files. So, if you want to add pics, just drop them in a folder (perhaps /sdcard/pictures/) and they should appear in Gallery. Sometimes they do not but the app RescanMedia will force a rescan and they should appear.
I personally find Gallery to be limited (cannot change the order other than from newest to oldest, cannot render the full picture when zooming in on a 12 MP photo, and a few others). I use QuickPic. It is free and you can tell it which directories to scan, change the sort order, better rendering and a few other features.
Those are shortcuts that may stick around for a little while but you could use the app RescanMedia or do a cold boot. The cold boot is non-destructive and the instructions are in a link below.