So I can feed my Ground plane or quad with a balun, then its a dipole?

no, it's not. be careful, you're making my case.

for a pair of quarter-wavelength wires to act as a dipole, several things
must be true.
physical arraingement, and feed are both important. your broken dipole is
somewhere between a real dipole, and the ground plane. basically, a
monopole, with a counterpoise.

if you significantly bend the wires, or re-arrainge them physically, then it
is no longer a dipole.

if we remove three radials from your ground plane, /i'm assuming it's fed
with unbalanced line directly, as it should be/ and straighten out the
remaining radial relative to the driven element, then we have your broken
dipole again.

there's another class of antenna, called a bicone, that has significantly
different charachteristics, but is conceptually very close to the dipole.
it's got broader bandwidth, and is commonly used in part 15 testing for that
reason. the discone is another very close relation, somewhere between the
bicone, ground plane, and a feedhorn.

this stuff does matter. when you make changes, they have effects, even if
your particular arrangement is too sloppy to notice them. when you make a
change that should have an effect, and it dosent, this is telling you that
you have other problems.

do you not see the difference between a driven, and a passive element

You think the end thats fed with the shield of the coax is passive?
Come on over and grab the end of my dipole, (fed with coax and no
balun), when I have 1Kw running to it. You will change your mind
about it being passive.

no, i won't. where did you get the idea that passive elements wouldn't have
current flowing in them. and where pray tell, is that current coming from

grab the director on a beam, and see what you get. that's a simple wire
sitting in space, with no connection to the coax at all.. is it a passive
element, absolutely.. has it got rf current flowing in it, you'd better
believe it.

your two wires fed in the middle with coax, are not a dipole.
the best name i can give it, is a monopole with counterpoise.
throw it into mininec, and see if you get the same results as a properly
constructed dipole.
that's freeware, a little limited, but it can do simple antennas like
dipoles with no problems.

you've also got a lot of rf current on your shield, which is making the
shield an active part of the antenna. you didn't think that this current on
your non-driven element magically stopped at the connector, did you.. why
would it stop there.. there is one possibility, that your feedline is an odd
number of quarter wavelengths long, so that this pont is high impedance. but
that only works at particular frequencies. in this case, it's still not a
dipole, /half the antenna isn't driven/ but it will work better than an
identical antenna with feedline an even number of quarter wavelengths long.

You will notice very little, or more likey no difference between a
dipole fed with or without a Balun.

like i said, errors in one area can obscure results in another area.

almost any damn thing will radiate and be tuneable.
a quick look at the antenna wall in the local truck stop will tell you that.

a proper dipole is resonant, given a balanced feed, and therefore does not
put significant signal onto the coax shield. /or it's fed with ladder line,
from a balun in your tuner/