.is there any place that buys old newspapers and magazines and pays me a small amount for that?
Answers:
If you actually have thousands of pounds (tons) of paper, you can sell it to a recycler for a nominal fee. You will have to transport it to a recycling center, but don't expect to get much money. Paper recycling is usually a losing proposition for most municipal recycling programs.
Check with the used booksellers in your area. Many of them will buy magazines, but unless you have old, hard to find, and in demand issues, don't expect much for your collection.
Good luck with your project.
Other answers:
Recycle!
Recycle!
Yes, it's called a recycling center. They will give you so much for each ton you drop off. Don't expect a lot of $$$, though.
If you have all your items catalogued, a bookstore that specializes in old newspapers and magazines may be interested. But only if you can put your hands on the issues they want very quickly.
Half Price Books buys magazines.