I would start your smart campaign smart list with "Member of Engagement Program" = True and whatever the name of your program is.
If you have 4 specific emails and you want the lead to have clicked a link in each email, then you would need to add a "Clicked Link in Email" filter for each email.
If you're saying you just want them to have clicked any 4 emails in your stream, you could just add the "Clicks Link in Email" trigger once, and add in the names of all the emails in your stream using the green plus button. Then add a constraint where min. number of times = 4.
To remove leads from an engagement stream, you add in "Change Program Status" flow step to change their member status for your engagement program to "Not in Program". Then you would need a separate flow step to change their lead status. You could also just pause the stream for the lead instead of removing them--then you would use a "Change Engagement Program Cadence" flow step. Choose the name of your program, and set the new value to "Paused."