Where can I download the full Stellar transactions and payments history? I have seen already that I can download one page at a time in the Stellar Website, but id like to do a full download since its inception.
You need to install a stellar-core server configured with CATCHUP_COMPLETE=true (otherwise it will only get the last CATCHUP_RECENT ledgers) which will download all the raw history from configured archives.
Then you'll need to install a stellar-horizon server and make it ingest all data from your stellar-core instance - which means it will process all the raw data from stellar-core into a more conveniently accessible database scheme.
Finally you can find all transaction data in your local horizon database (usually postgres) and also access it via your local horizons api.