Yes.  Hopefully you will have other money or income to live on.  You may need to wait longer than 65 to get your full Social Security amount.  But at 65 you need to sign up for Medicare.  

Yes, you don't have to apply to start your SS benefits until you want them, even if you stop working earlier. 

If you re going to stop working you should also consider what you will be doing to have healthcare.   You are not eligible for Medicare until you are 65  (except for some special cirucmstances)   so you need to know what you will do for healthcare if your healthcare has been provided by an employer plan.