if a new website now ranks good in google after that long delay for a keyword . then later on I add a page to my this new site for some other keyword and make good backlinking for this subpage would it too go down to the last and again require that long delayto cpme up in SERPS??
Since your main page finally doing good, it can help your new subpage. Aren't they closely related/relevant?
No it won't once your site becomes free you can add as many inner pages as you want and they will rank in the SERP's based on the inbound links to that particular page as well as the keyword competition. so good luck.