1) You may visit any site that shows you the (public) IP address your request comes from, a common example being http://checkip.dyndns.org/
Edit from 2020: Some more information can be obtained by going to https://ipinfo.io/ - that can give you a hint on which connection is being used - if you see the name of your private ISP there, or the name of your company, you might get an idea which way your request took.
If it shows the same IP while you're connected to the VPN and when you're disconnected, your traffic seems not to be routed through your company's VPN. The IP address shown will be the one assigned to your home internet connection.
Also, on a Windows computer, you may open a shell and enter "route print" - which shows you which "way" traffic destined to different networks will take. Usually there will be a so called default route, which is first in the list and 0.0.0.0 0.0.0.0 and has your local ISPs router/modem as a Gateway address.
After connecting to the VPN, do another "route print", and notice the differences in the routing table - the new entries will most likely have a Gateway address associated to your VPN.
2) If a VPN connection routes every traffic, or only specific addresses (usually private addresses used at home or in corporate networks), depends entirely on the configuration applied by the VPN's administrator (or sometimes on configuration applied to the VPN client).
The reason can be a very easy one - usually only traffic to your company's Intranet needs to be routed through the VPN, as those addresses are not publicly accessible. The "common" traffic - everything publicly available via your home internet connection - has no need to be routed through the company's VPN, and just consumes bandwidth on your company's WAN link, processing power on the VPN endpoint and so on.
Nevertheless, some companies might still route all traffic through the VPN, be it for traffic inspection, some kind of security rule, or because the employee may be based in a country where internet access is restricted/monitored, so these restrictions or dangers can be avoided.
Best Answer
Figured out.
Installed this:
https://supportcenter.checkpoint.com/supportcenter/portal/user/anon/page/default.psml/media-type/html?action=portlets.DCFileAction&eventSubmit_doGetdcdetails=&fileid=10655
Then run Internet Explorer as an Administrator.