If I have my website created with a third party company and they are infringing any patent, could I be sue, just to be a user of that software or program?
My father, who owns an ISP, was recently sued for patent infringement because he provided DSL (a type of internet over phone lines), and a patent troll who owned some patents regarding DSL sued him for purchasing and selling to his customers a particular brand of DSL modem.
So, you can be sued. The case was unsuccessful, as there were license grants that trickled down to the DSL modem manufacturer that included the patent, it was simply difficult to trace back.
This was a case of a patent troll looking to farm settlement money, but it still costs a reasonable amount of money and time to defend against such things.
Yes , A patent consists of two parts - method claims and system claims. If you are third party using an infringed product you are susceptible to being sued by the method claims of the patent .