hello,
Radials is a story on its own.
To all your questions, the short answer is yes.
The longer anwer would be something like:
All vertical endfed antennas need some type of "radials".
Though for some the demand for it is higher then others.
Again: ALL vertical end-fed type antennas needs some sort of radials.
(this includes the antron 99 types).
Often you dont see it as "radials" as it uses the coax or mast to act as part of the antenna, and some antennas can 'get away" with relative minimal amount of radials. The demand for your halve wave vertical isnt that high ...so there is no need to extend the length.
In some cases the need for those radials are more demanding.
As soon as the current is high at the feedpoint radials will have a large impact on the antenna.
This is almost always the case if the antenna is not a end-fed halve wave.
The reason for that is cause the current is high at the feedpoint.
And on a end-fed halve wave the current is relative low at the end and you can get away with short radials to let that current flow.
How do you know if current is high ?
Well, we know at the end of the antenna resistance is high.. .there is air..
Ohms law tells us : U= IXR.
Now we need to draw the 11 meter "wave" back from the top of the antenna towards the feedpoint.
If R is high that means I current is low and U (voltage) is high again.
here is an example of the the halve wave with the current displayed:

Thats easy...at the end of the antenna.. current is always low so you can draw that wave back to the feed point and find out.
At any place where that current is high demand of radials is high too.
If we take your groundplane... that is 1/4 wave long... we are in the middel of the above picture.. current is high.
All antennas that are not a end fed halve wave ( or any multiply of a halve wave have got relative high(er) current.
That current needs to flow somewhere...so theres a need for radials with 1/4 wave and 5/8 wave kind of antennas.
But its "up to a point".. The first couple of radials have the most impact obviously.
Just think about that mobile antenna without a car.. that wont work efficient at all.
Oke, now if we have a normal groundplane and place it well above earth and has sufficient radials at a 90 degree angle from the radiator the impedance will be ideally roughly 36 Ohms. If change the angle of the radials and put the at a 125 degree angle the impedance will rise to 50 ohms and we can find a nice match !
Thats the reason why lots of 1/4 wave antennas have those radials in an 125 degree angle.
So yes, the angle can change SWR.
If we take that groundplane with radials again at 90 degree.... you could also remove radials... say we have one radial at a 90 degree angle the impedance will rise again from that 36 ohms. The same happens if we shorten the radials... the resonant frequency will shift higher and impedance will rise.
So, yes the length and amount of radials can change SWR.
I dont know the radials you mentioned.
How long are they ? And how many ?
.....Important to remember .....
You could actually tune the 1/4 groundplane for better SWR by reducing the amount and length of radials. BUT you will also REDUCE the efficiency of the antenna, which is not a good thing.
A "worse" SWR in that case is actually a more efficient antenna.
Radial length will also effect SWR, but overall you could say they need to be a quater wave. Why ? well... you want maximum current in that system...and that better with a sufficient amount of radials and a quaterwave (or longer).
The goal is to go for maximum efficiency instead of best SWR.
As you can match SWR...you cant "match" efficiency.
That is unless there is almost no current at the feedpoint...then the radials can be shorter as is the case with your halve wave vertical.
With the above said, there is a correlation between the amount of radials and length. And there is with how high the antenna is placed.
If the antenna is sitting on the ground the need for radials increases.
Thats one of the reason why broadcast MW stations have a hugh amount of very long radials underneath the tower (which basically is a 1/4 wave groundplane).
Kind regards, Henry