the security warning is really nothing to worry about. it just means that the website isnt using an https url. what this means is that personal information like passwords is encrypted, or basically turned into an unintelligible code that potential hackers, if they really felt like hacking the website to begin with, would hopefully not be able to read.
if the website starts with http, that means passwords and stuff are not encrypted. most websites generally are http, even those that require passwords. obviously websites like banks and stuff would use https.
the website is not being attacked by hackers. you are not in danger by entering your password. nothing will happen to your computer
though because most websites are not secure, as a general rule you should use a different password for every website.