Re: few questions about router settings.

#1

Part a) yes if it t is the Default OR any computer has malware (or had malware on it recently).

Part b) Also see the text at http://ask-leo.com/should_i_change_my_routers_password_and_if_so_how_often.html

 #3 No, see http://www.howtogeek.com/howto/28653/

Title Debunking Myths: Is Hiding Your Wireless SSID Really More Secure?

[EDIT] #2 See the posts above mine in this thread