"on edge" means nervous about something

'off the cuff' means that the opinion you are about to express is one that you have not had time to think about : 'my reply, off the cuff, is that . .' 'on edge' means nervous, anxious : 'he seems to be rather on edge this morning'. 'nip the uprising in the bud' : to 'nip sthg. in the bud' means to suppress, contain or extinguish it before it develops further, before it gathers momentum or gets out of control. In this case it refers to an 'uprising' - a revolt or rebellion by people against sthg., probably an authority, government, or organisation that has power and control over them.

the second part of your question doesn't make a lot of sense - onedge isn't a word - did you mean to write 'on edge'? To nip something in the bud means to stop it before it develops very far.

Off the cuff means something spontaneous, for example i was a best man at a wedding, i didnt prepare a speech i did it off the cuff