As I have post count less than 100, my signature should not be visible to others, right? But I could see that. Is my understanding correct?
No your understanding is wrong. Its visible to everybody but you do not get any benefit out of it in search engines unless you have your post count in triple digits. Yes all the sig links would be do-follow. Old as well as new. The reason we have implemented the same is because we are among the top spam lists because some of the threads also get PR3 to 4 easily like my article Design pattern in simple examples
Search Engines follow an attribute in a link called rel="nofollow" which if added SE bots would not follow the links on the pages and this is added to the signatures if any user has post count in 2 digits or less
this was a great idea to not to let crawlers follow the link unless post count is in 3 digits to check if the user is legit. kudos for shabbir.
Its because of the cache of your signature and try saving it with a minor edit and you will see the new one being reflected everywhere.