Looks a one to me. Use the swept tees and deburr the copper after cutting. Balancing your system once new rad is fitted will be necessary and yes, that's the drain, you could add an extra drain when fitting the rad. Think about Autovents when fitting the new rad.
If I read your diagram correctly, which seems to miss out the boiler and pump, your suggestion to extend is absolutely correct.
Make sure the rad pipes come off the one pipe vertically, buy large bore TRVs (not the standard ones) and all should be well. The balancing valve suggestion is misinformed, to put it as politely as I can.
And you don't really balance a one pipe system, the rads get warm by the change in density of the water mainly.
As you point out, the other rads work, so if all the suggestions in this rather shameful thread of 'expertise' are valid, how come?
If the two pipes teeing off the radiator in this photograph
form a loop with another radiator like this..
Then you do have a one pipe system, albeit a bit unusual, but it does correspond with what is visible in your photo, the bit under the floor of course is unseen.
However, the photo below doesn't quite fit in with your 'one pipe' drawing though, where all your radiators sit atop a single loop. It is possible that you may have some kind of hybrid where parts are two pipe and parts are one pipe, but without being able to see exactly what is connected to where it's impossible to say.
If you need to find a tradesperson to get your job done, please try our local search below,
or if you are doing it yourself you can find suppliers local to you.
Select the supplier or trade you require, enter your location to begin your search.
Please select a service and enter a location to continue...
Are you a trade or supplier? You can create your listing free at DIYnot Local