Non-correspondence of voiceless stops in several IE languages

Hello, this is my first post in this group.

Since some time I am intrigued about the apparent non-correspondence
or
confusion of some (mostly initial) voiceless stops in several Indo-
European languages. To understand what I'm talking about, the most
notorious example is the word for "five", which is thought to derive
from the PIE root *penkwe. In all these words we find 'normal'
reflexes:

Lithuanian penki
Latvian peci
Sanskrit pañcan
Albanian pesë

However, in most cases we find that one or both stops of the original
root (p, kw) have changed into different stops.

Here the kw changed to t:
Greek pente
Proto-Slavic *pet (with nasal 'e' and the "strong" jer after the t)

Here the kw changed to p (yielding f in Germanic):
Proto-Germanic *fimfe (Gothic fimf)
Welsh pump
Cornish pymp
Breton pemp

It seems that the p, p sequence should be present in all the Celtic
group, but the Irish "cúig" suggests a preservation of the final
velar
and a change of the initial p to k (or kw).

Perhaps the most studied case is the Latin "quinque", which shows a
change of the initial p to kw. Some explain this through assimilation
of the second syllabe to the first one. But Irish and Latin are not
the
only languages in which we find a change of the initial bilabial (p)
to
a velar (k, kw), we also have Armenian "hing"'.

I would like to know if this change of initial p to k is common and
whether some linguistic rule could be applied to it. In Spanish we
have
at least one case of the reverse change: Latin "columba" yielded
Spanish "paloma", 'dove'.

Furthermore, I see a strong similarity between Latin "cado,
cadere", 'to fall' and Proto-Slavic "pado, pasti (pad+ti)", 'to
fall'.
The PIE root *kad has been posited with the meaning 'to fall', but it
only can be applied convincingly to the Latin root cad-, Sanskrit
sad- (with "accented s") 'to fall' and Greek "kata", 'down', while
the Slavic pad- 'to fall'
is
not usually linked to it, though I think it should.

Thank you in advance for your comments.