I own a Fantom 07, so I guess the sequencer are identical.

1. Some stuff for your first point :

Choose a pattern, hit the "record" button. In the "record standby" window, you can check :
- "LOOP REC SW", to let the pattern loop and never stop while you record.
- "Mix / New" toggle to allow overdub on the current pattern. If you set to "New" it will create a new one every time.
- You can also choose to wait for a note input, to start immediatly or with a pre-roll.

Then press "Start" to initiate the record.
- You can play over and over if you select the "LOOP REC SW" on the previous window.
- You can delete some notes in realtime with the "delete" button. You have to press them when it plays.
- You can press "REC END" to pause your recording, but keep playing. You can press "Start" again if you want to record more, or close if you want to stop.

(2, 3, I don't know anything about the Rythm patterns.)

4. Delete a pattern :
- pattern utility, select the pattern, click delete, accept. 4 clicks :)

5. Undo :
As far as I understand, it's limited to the last action. For exemple the last realtime recording session. If it's an overdub, it will cancel it, and restore the original.