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.