I know similar questions have already asked but I think we need something slightly different:
Do you think SalesForce can provide this to us? Or do we have to write our own or tweak an open source application to do this.
It's a good question; unfortunately the answer is complex.
"Salesforce" is a platform more than anything. Out of the box it doesn't do much; with customization, scripts, and for-pay add-ons, it can literally do anything.
There isn't an open-source tool which will do all this stuff out of the box -- again it takes customization, scripts, etc.. Is it cheaper to have zero-cost tool but write and maintain more code, or pay more money monthly but buy stuff that does most of this now? Either choice is OK -- that depends on your goals.
* Capturing user info from our website to the CRM directly via an API
* Other CRM, Leads management stuff
Not sure about API, but can provide access to stats; integrates w/ Google AdWords, too, if I remember correctly.
* A way to either pull stats out of it via API or provide limited accounts to our employers so they can see all our demo, sales, leads stats in real-time
I don't remember the cost, but to get some of the features above, you have to buy one of the more expensive account plans.
* Not insanely expensive
**FWIW, This info is based on experience that is several years old