Your friends are (a little bit) wrong when they say :

je vais amener des bières.

This is considered as familier. The primary meaning of apporter is :

porter avec soi quelque chose dans un lieu.

The primary meaning of amener is :

faire venir quelqu’un avec soi.

The difference relies on the difference between porter and mener, the prefix a, added in the 2 cases, is herited from ad in latin, which means en direction de if I remember well.
Porter means something you can have in your hands (roughtly, not a living thing), while mener refers to a entity that can walk beside you, follow your steps.
There are some exceptions : amener can be used for some non-living entities :

son caractère l’amène à être violent

son caractère is considered as a kind of living thing.

While apporter shouldn’t be used for living entities unless when they are considered as object:

J’apporterai des poules pour le repas.

versus:

J’amènerai mes poules pour que vous voyiez comme elles sont belles.

but we won’t eat them !
Cheers.

if you look up the words amener and apporter in dictionaries, you will see that they prescribe that apporter should be used with objects, and amener with persons. Using amener for objects is considered as familier.

In everyday usage, you can indeed use amener for apporter, and no one will frown upon that, it will not be considered as “bad” or “uneducated” French. You will hear that in conversations among friends, but also at work, in schools, etc.

Ex:

J’amènerai des bières/J’apporterai des bières

are both equally acceptable in a common, everyday conversation.

BUT note that the opposite is not true: you cannot use apporter with persons.

Ex:

J’amènerai une amie à ta fête

is OK, but

J’apporterai une amie à ta fête

is incorrect, or awkward at best (it would imply your friend is inanimate, or dead, or that she will be so drunk that you will need to carry her on your back – but that is really far-fetched).

So as a rule of thumb:

• in an essay/formal letter/formal speeches, etc: stick to apporter for things/amener for persons

• in everyday speech/friendly notes/text messages, etc: feel free to use amener for things

As for the distinction between amener/ramener, apporter/rapporter, you are right that the first meaning of ramener/rapporter is “to bring back to the original location” or “to bring again”, as the prefix “r(e)-” indicates. Now, you can also use it in the sense of “to bring along as you are going back to the place where you are coming from”. Let me explain with some examples:

You are at a party with friends, and you want to go the grocer’s to buy a pack of cigarettes. A friend may tell you:

Si tu vas au magasin, peux-tu ramener quelques bières ?

Of course, you would not “bring them back”, but you would bring them along, as you are coming back from the grocer’s.

Or: you are coming back from a trip to London, and you have bought a t-shirt for a friend. You may say:

Je t’ai ramené un cadeau de Londres.

That means you have brought this gift along as you were coming back from London. You would not use ramener in this case if you live in London.