Alfonso says...

Now to any sensible person "The frequency of a transverse moving clock
is reduced". means a clock moving w.r.t you - it wouldn't be moving in
its own FoR would it? So "b/ The time interval between ticks is
increased" is clearly referring to the same transverse moving clock as
in a/ but for some reason you need that explained to you ... yet when
Einstein says "if an observer is moving with velocity v relatively to an
infinitely distant source of light of frequency f" in section 7 you
consider it is perfectly clear from section 3 which is the direction of
v.

The whole paper is explaining the derivation of and the implications of
the Lorentz transformations. He introduces the two frames K and k at
the beginning of the paper, and every section returns to these two
frames.

Section 7 starts off:
"In the system K, very far from the origin of co-ordinates, let
there be a source of electrodynamic waves..."

Then a few sentences later:
"We wish to know the constitution of these waves, when they are
examined by an observer at rest in the moving system k."

It's certainly possible that someone by this point has forgotten
the definitions of K and k, but that doesn't make it ambiguous.
If I'm reading Romeo and Juliet, I might forget whether
Benvolio is Romeo's cousin, or Juliet's cousin, but that
doesn't mean that it is ambiguous whose cousin he is. It's
right there in the play.

--
Daryl McCullough
Ithaca, NY