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So because Apple ( the makers of the iPhone and iPad and Mac) and Google (the makers of chrome, and chromebook, and android OS) are 2 different companies, and the fact that Apple keeps everything proprietary, the best way to sync all of your personal data (contacts, web links, homepage, login and other info) is to use a single application.
Apple has this, but it wont work on anything but an Apple device, and Google has this, and theirs will work on ALL devices.
So, I would reccomend you use what google has to offer for managing personal info.
YOu can use the Chrome Browser, on all Apple products and that will remember all your web links and browser information.
YOu can use google contacts, and that will remember all your contact info.
You can use Gmail on apple devices too. Which will be used for all your email.
Ultimately, google plays well with all other companies and google has made applications that work on Apple devices, and windows devices.
Making google the logical choice ere for syncing across different devices.
im going to opt out now....best of luck to you.
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.
I have also submitted to our moderators your refund request in hopes to help you with that too.