What are the best UX practices for integrating a website with a call center?

I value your request for help. However, my experience is that a straight barter of design services for development services is not necessarily equitable, as design is most often a fraction of overall development effort and cost, albeit, design is critical and sets the stage for success in a project. At DVmobile, we believe that the first 15% of a project (including design) is what make the remaining 85% of a project successful. Bartering often implies very low revenue potential in the relationship. It begs for similar circumstances in your partner, a willingness to work for services vs. cash payment. My recommendation would be for you to attract multiple partners that can leverage your services on a part-time contract basis. If you are attracting customers with your design skills, many development firms, including mine, are willing to do subcontract or partner based work. It’s usually easier to market great design skills in today’s market, than coding skills.

I have used this https://canvanizer.com/ for my venture as well as for other clients. Feel free to contact in case you need to get more details.

You can of course use analytics that will give you statistics, but will not answer "Why?". Gathering Customer Feedback is crucial and You have to be preprared for low response rates. For better understanding of Customers' interactions with Your site You can use tracking/heatmap solutions (i.e. Crazy Egg or Hotjar). But most important is to define goals and identify steps that lead to them - what do You expect Customer will do or act like? What needs to be done to acheive it? Then start monitor those steps, gather feedback, mae changes and see if this works looking at stats.

I thought questions was for ... questions...sure I'll send an email when I have time.

This would really depend on your goal of the lead channel. If you want to deal with warm leads give http://inspirebeats.com a try. InspireBeats will help you find and build a list of targeted leads, do research on them, and warm them up for you through a personalized outreach. That way you have an additional channel of leads flowing in for your sales reps.