Yes, you can upgrade the firmware to the latest asuswrt-merlin an use the OpenVPN client to connect to an OpenVPN server, or directly you can connect to a PPTP or L2TP VPN Server on WAN Settings, i've tested both and it worked very good.
Not really sure I understand your question. VPN is a "secure tunnel between your computer to a known server that is running the same VPN software". So when you say "securre browsing" what do you mean? Within the secured VPN tunnel? If that is your question then yes. Just a little confused by your question.
Yes, you can do this. Your remote machine could VPN to the router and browse via that tunnel encrypted to the internet. This router works as a VPN server and you don't need any local machines on the router side to accomplish this. HTH.
The VPN server on this router is for securely connecting to your home network from a remote location via a secure connection. If that's what you want, then I guess It does. What is secure browsing? There is always some risk when browsing. No matter what you hide behind. Stupid is what stupid does. Once your connected to the internet it doesn't matter if your browsing or not, your IP is still connected. You should be using a firewall in addition to the one built in to the router.
Through VPN, you will be part of the local network (e.g your office) as if you are sitting there, you can browse through the internet line of that network . If that line is slow, so will be your browser speed. No computer in that network needs to be on. If they are off, of course you can't connect to any shared folders of them.
ASUS routers support quick VPN setup so you can keep your full online experience wherever you go. Take a look and see it done in just a couple of minutes!
http://www.youtube.com/v/dsbbae19tB4 <- Copy and paste in your browser to see a video tutorial of about 2 1/2 minutes. Its pretty straight forward. Hope one or the other has what you are looking for. Your question was pretty 'generic'.
If that hasn't what you are looking for browse this and see if it has any information in regard your question: " Granite Bay Golfer asked "Can I use this router's vpn capabilities for secure browsing without any of its local computers active (i.e., router itself is sufficient)?"