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.
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.
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.