Well it will save your account information if you agree to save it but if you not then you'll need to retype it again if you are logging in which is recommended for our accounts safety, i think cookies has less work about the credentials and it is more about our browsing activities. I think it is just simple, if possible do not use public computers in accessing your wallets or exchange site you stored your money but if not then make sure to watch yourself from clicking too much so that your account will not be in danger. If you have your own device, laptop or phone you can save your account details for it is only you who will use that device.
Cookies save the passwords so that you don't need to ever login and just type the URL like gmail to login your email account. Phones can be hacked easily. It saves your credentials. Recently uninstalled my browser, deleted my cookies folder and had to login again to all the sites where I was previously logged in.
There are popup ads nowadays which directly get installed on your computer and are malware. I detected one recently and had to delete it. In public places there are CCTVs as well so they can take a note of your password as you type it. I have noticed people even peeping in your device while you are typing your phone password.
AFAIK you can choose to synchronize your passwords with your Google Account so you have access to it from other devices. So, yes.
It's only if you sync else it's saved only on your device. Best is not to sync.