How to see the behavior of users on a website?

NO, there no current tools available.

Try Intercom.io You get visitor level information on how active they are etc.

Google Analytics is the best free tool out there for this. Make sure that you are focusing your report on conversions - how many/what percentage of website visitors are taking action (filling out a form, buying a product, etc.). If you're interested in paying for help, you should check out Moz or HubSpot, but Google Analytics is your best free option for web reporting. They also provide some social reporting - which social networks are driving traffic to the site and which network referrals are leading to the most conversions. Good luck!

Top 2 tactics: Existing Users and Industry Influencers. First, leverage the existing user base. Incent referrals with $5 for every new free user they get to sign up and start using PT Engine for a new domain. Second, reach influencers and offer them the same deal when they tweet / post to / email their audiences. Make the offer a 60 day free trial instead of the standard 30 day so that they are providing value to the people they refer as well. This is critical - don't make them feel sleazy, make them feel (and look) like heroes to the connections they share PT Engine with. That's $9k to get 1800 users, leaving you $1k for graphics, referral tracking system, administrative costs. I assume the $10k budget does not include your time - if it does you'll have to reduce the incentive, which will definitely make it less appealing. If you want to dive deep on reaching influencers, schedule a call with me at www.clarity.fm/ryandraving

Sorry to be a bit blunt in my answer, but the client hired your "e-commerce web agency" to do e-commerce conversion optimization, yet your company doesn't know how to do e-commerce conversion optimization? Perhaps have a conversation with someone in your company or talk to your manager or the agency principal and encourage them to hire for e-commerce conversion optimization expertise. It's an entire discipline requiring years of experience and track record in driving higher conversions for e-commerce sites (in my opinion). In lieu of that, how many marketing dollars are going to be spent to drive traffic to the site and who is managing that part? Often new start-ups will spend so much of their dollars BUILDING the site, they don't leave much money to spend on AdWords or other methods to drive traffic to it. The amount of traffic will help determine how many tests to run and how often. Usually we start with two very different landing pages (do you have landing pages?), then fine-tune the split testing down to things like headlines and photos. The checkout pages, especially any pricing pages, are also critical in the testing. Is it a brand new concept or established product/service? If brand new, it will take very well-crafted pages to get visitors to pay money for something (vs. a trial). If established, why is your product best and why should I buy now? You should map out the conversion flows to the confirmation page (success page) and measure the drop-off or conversion rates at each step. Test different elements/pages at each step. Also measure things like average cart size (if more than one product), revenue per transaction and long-term customer value. Hope that helps. Best wishes to you!