Samsung Galaxy S4 Active — Cookies - Browser?

Hello everyone,
I am using a Samsung Galaxy S4 Active and I am not very technical, and am well past my sell-by-date!
I have just created a new email account and downloaded the app for it onto my phone.
I cannot open it as I am informed that my browser does not allow cookies.
I have taken the phone to a tech shop and he told me that I cannot adjust the phone to accept the app’s cookies to allow the app to work.
1. How do I access the browser and does it have a name.
2. If I am able to "allow cookies" will they be of any danger to my phone.
I have tried to update my phone but each time I am informed that it is up to date and has the latest updates - (I've had it for a couple pf years and it has never accepted any updates!)
Any advice on how to get the app to work would be gratefully received!
Thanks,
Colin.