I stress that I'm not involved in this project at all, and thus my answers here are pure educated guesses, but I am a railway engineer and a chartered member of ICE, so here's my thoughts...
Given the timescales that this job was done in, the calculations to work out how many piles would be genuinely needed would take too long, and would involve some pretty big assumptions about the ground type anyway. If this were a project on a normal timescale you'd do some robust ground investigation, but there's no time for that here, plus the ground is known to be settling/moving/substandard because, well...
Accordingly, the design methodology is likely to look more like 'take whatever information we can glean from similar situations and any records we have available. Make some pretty generous assumptions about the loadings and the ground stiffness and stability. Work out the resultant number of piles required. Double or even triple it if the assumptions were big. Go for installation.
Almost certainly 660mm diameter as this was one of the most common pile types used on the electrification project, and thus is probably what was in a store somewhere. The piles look very much like leftover electrification foundation piles - look at the tops - those are screw fixings for OLE mast brackets.
How long - piles were frequently up to 5m long, sometimes longer, so probably about this.
Length was probably also 'driven to refusal', or driven until they were presenting a certain resistance force. By doiing this you can install to a reasonable level of confidnce that the piles can bear a certain amount of weight, and thus would be suitable for the temporary scenario.
This is also supported by the pile tops all being slightly different heights - being driven to a force rather than a depth would mean they all reach that force at slightly different points.
Almost certainly vibrated or hammered (or a bit of both) down. You're putting these into a river bed so you really don't want to be boring or augering if you don't have to.
The designers probably only had a very rough idea of what they could expect for that, hence my above assumption of driving to a force rather than a depth.
Unlikely. If they were filled they would be filled with concrete, which would make removal much harder. Given these are temporary, almost certainly with the river authority demanding a removable solution, you want them to be able to be removed fairly easily, or, if they refuse to come back out again, able to be cut off at the river bed.
My best guess would be something like the 'superprop' from mabey:
https://www.mabeyhire.co.uk/MabeyHi...ropping-and-Jacking-Brochure-web.pdf?ext=.pdf
Probably a plan to cut the tops of the piles off at the same level and place some props across the top.
However, there's a plethora of options for this one.
They would also almost certainly have lots of monitoring sensors on the piles and props to ensure he piles don't shift too much when they are loaded.