I was reading through your questions and want to provide you the assistance you need. Based on what I can tell your goal is to create a seamless experience between your iphone, ipad, and chromebook.
To answer your initial question "Can I sync contacts, on line banking info, etcetera, onto the Homepage aera of my Chromebook?" The straight forward answer is unfortunately no. While you can create links similar to bookmarks in this area to point you off to the right websites, this wont store your login data, or your contacts in a straight forward manner.
So what is your options? Chromebook is a unique operating system. It's not meant to be a full featured laptop, but really a portable web browser. So everything that you see and feel in a chromebook, even if it looks like its a real "app" is actually just a chrome webbrowser in the background. The only true way to sync data between these devices is to use chrome on all your devices. For example, if you use chrome on your ipad and iphone, the history of the websites you visit, and the passwords you tell your ipad and iphone to remember while using chrome, will carry over to your chromebook. This is due to the sync that chrome does to your google account. It's important, however, to make sure that your iphone, ipad, and chromebook are logged into the same google account.
Similar can be done for your contacts, again dependent on you using the same google account. Apple has provided a pretty good article on this https://support.apple.com/en-us/HT202302
Overall what you are going to find is if it can't be done in a chrome browser, it wont work on a chromebook.
Hopefully this points you in the right direction, let me know if you have further questions and i'd be happy to help.