As I read in this blog article, in a blockchain "each node has a copy of all transactions ever made". This to me seems impossible, bitcoin has existed for a long time, and the memory size of the entire blockchain would be enormous.
ps: if I have to pay for a service using bitcoins, do I become a node of the blockchain?
To join the network, a Bitcoin full node will work its way through the network history, independently verifying the state of the network through time. So yes, each node will have downloaded and validated the entire transaction history, but a node can choose to use 'pruning mode', where it will discard unneeded transaction history after validation is complete.
The ever-increasing size of the blockchain is a heavy consideration when considering network and protocol updates. Bitcoin requires a distributed network in order to maintain its function, so it is important that the software can be run on inexpensive hardware, so that more people can participate.
ps: if i have to pay for a service using bitcoins, do i become a node of the blockchain ?
There are other ways to interact with the network. Many wallets are lite-wallets, which validate the chain via headers instead of the entire block. This is a less robust security model, but it works well for many people.
You generally do not need to pay a service in order to interact with the network (as a full node, a lite-wallet, etc).
Full nodes by default store the entire blockchain. The current size of the blockchain is ~250GB, so it is feasible for individuals to have their own copy and verify all of the transactions. There is also the option to run Bitcoin in pruned mode, which reduces the number of transactions that need to be stored. This greatly reduces the storage space demands and it can still verify all the transactions.
However, not every node is a full node. There are lightweight nodes known as SPV nodes that don't verify the entire blockchain. Instead they can verify block headers and rely on a full node for the state of the blockchain.
More info on SPV nodes: https://gist.github.com/ariard/1034cd7624805d53334e80d4712fb8ee
If you're paying for a service using Bitcoin, its very likely that the service provider is running a full node for you. You run your own node when you run the bitcoin software yourself. It's a a worth while experience and if you're interested in Bitcoin and want to help maintain its integrity you should consider running your own node.
What/how to run your own node: https://bitcoin.org/en/full-node#what-is-a-full-node
