Thank you for your post.
This can definitely be set up in FileMaker Pro, but it will take some time. You can definitely link tasks to customers, suppliers, and set up emails and automatic sending of emails. Inventory can definitely be done.
FileMaker Pro will not link to iCal unless you purchase a additional third-party plug-in.
There are sample templates that deal with Inventory, email management, Contact management, event management, Purchase Orders, Task Management, and several others. Some of these would be a good starting point.
I would download a free 30-day trial from our web site (www.filemaker.com), create a new table based on these templates and begin working from there. This should give you a good start to see if FileMaker works for you.