I would like to call /network/points against one of the public nodes. I tried curl -s ipaddress/network/points after I got the addresses from Giga Node https://tezos.giganode.io/, but it returns nothing. Are there basically public nodes and how can we run JSON-RPC against them?
Giganode is indeed a public node, among many out there. However, not all RPC endpoints are exposed for performance and privacy reasons. For instance, https://mainnet-tezos.giganode.io/network/points returns 403 Forbidden because they don't allow it.
If you are looking for a list of tezos nodes, you can use this popular script to get more nodes from TzKt.io and add them to your node.
As an alternative to public RPC nodes, MIDL.dev offers a commercial Tezos RPC service.