Can I embed the client web calendar in my own web site?

Yes, you can. The client calendars are nothing more than a web page that we host on our servers. They have a URL (link) that can be used anywhere. You can find the URLs to your client calendars in the app's settings > Online Booking > Details & Settings (see image). They have the following format (the last part of the URL will be unique for your business):

http://bobclass.com/classes/c4fit 

http://bobclass.com/appointments/c4fit

Pick the one you want to share with your client and use it as a simple link on your web page, i.e. a simple "punch-out" to the web calendar. Alternatively, you can embed the link into your page. This requires a bit of simple HTML editing using a so-called iFrame. If you do not know what this is, ask any web developer who can add this to your website. This way, the calendar will sit nicely in your own page and you do not have to punch out.