What if i need to use a different computer other than my own to log into a site requiring 1password to log in? How does that work if 1password is not installed on that computer?? Would I still have to remember the website's password anyway then??
If you sync via Dropbox, you can access your data on the Dropbox web site with any modern browser and use 1PasswordAnywhere.
While there is 1PasswordAnywhere that you can use, do not use it on computers you do not trust fully. If you can not be sure that the computer does not have malware or key loggers, you will risk exposing your data such as your Dropbox.com and 1PasswordAnywhere information. You can find out more here: https://blog.agilebits.com/2014/08/21/watch-what-you-type-1passwords-defenses-against-keystroke-loggers/
Only use 1Password on computers you trust and try to use 1Password on smartphone or tablet if you have one. The reason is that you don't need to give up your Dropbox or 1Password information because it is isolated to your device. You can manually type in the password on the untrusted computer and only risk exposing that specific site instead of the rest of your data.
Make sure you also use VPN on untrusted computers as well.