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Google Chrome is a browser application, just like Safari. If you don't wish to use Safari, then you can use Google Chrome. All you have to do is download Chrome from App Store and use it instead of Safari.
Remember, there is no option on your iPad to make Google Chrome as default browser. For eg, even if you have Google Chrome installed on your iPad, when you open certain links like the links received on emails, they will still open in Safari. You have to manually open them in Chrome. This is how Apple designed it.
If you want to set Google Chrome as default browser on iPad, then you will have to Jailbreak it and install a third party application to make Chrome default. See here --> https://en.wikipedia.org/wiki/IOS_jailbreaking
Jailbreaking the device will device will void all support and warranty from Apple. Also, jailbreaking the iPad is illegal. But it will grant you a variety of features, options and flexibility over apps.
Your last question is not very clear - "Is there any way to do this on my desktop Mac ?"
Do you want to download Chrome to your Mac desktop ? If so, it is possible and on desktops, you can set Google Chrome as default browser.
You can download Chrome on your Mac from this website --> https://www.google.com/chrome/browser/desktop/
If you have any questions or would like any additional information, please don't hesitate to ask.
Please note that this is not my final answer. If you have any more questions, please feel free to ask and I'm happy to answer all your questions until you are fully satisfied.