...as for the other details: - "Flight Level 380" means 38,000 feet altitude (roughly) - "Estimating DOGAL 07:07" - DOGAL is a navigation waypoint off the coast of Ireland, so the pilot expects to reach that point at a time of 07:07 - this is early morning when many of the east-bound flights arrive from north America. The Air France pilot is using a different waypoint called SIVIR which lays to the south. - "CPDLC" is Controller-Pilot Data Link Communications which is a sort of text message system used between controllers and aircraft - google it.
...and the one near the start is a Lufthansa flight (who appears to mess up his callsign readback). The VHF frequencies given are for the Shannon and Brest control sectors which the flights will contact as they enter those sectors of airspace. The musical pings are SELCAL transmissions which you can google if you want.
This is a ham operator on the 20 metre band calling CQ ie a contact request (CQ = Seek You). He's saying: >>> Calling CQ, calling CQ, calling CQ This is October November Seven Hotel Lima United [he then repeats variations of this] <<< His phonetic alphabet varies during the transmission and is non-standard! The first letters of his callsign identify him as a ham operator from Belgium.
Sounds like Radio Teletype (abbreviated to RTTY, pronounced 'Ritty'). Basically hams sending each other text messages at incredibly slow speeds. It's similarity to an old modem sound is no coincidence because that's basically what it is.
This isn't ham, it's Shanwick air traffic control which controls the oceanic airspace for the Atlantic air traffic (roughly) west of the UK and Ireland. The callsigns are individual aircraft eg 'United' is a United Airlines flight. Near the end there's an Air France flight.