Quick explanation:
Let's make a clarification about the use of "podría". Podría is the verb
"poder" in conditional tense would, translatable as "can" / "could", "may", "be able", depending
on the context. The desinence "ía" is what gives its conditional
conjugation. But you wouldn't necessarily use this verb to ask
something in the conditional mode:

"¿Podría darme una servilleta?" corresponds exactly to:

"Could I have a napkin?" or "May I have a napkin?" or more literally
"Could you give me a napkin?"

But there is still to consider the equivalent to:

"Would you give me a napkin?" which is:

"¿Me daría una servilleta?" where the conditional form is given by the
desinence "ía" added to the verb "dar" = "to give"

Long Explanation:

One major difference between English and Spanish is that the latter is
strongly desinencial, so it doesn't need auxiliary verbs to construct
tenses, as English does (in this case, "would"). Now, this conditional
form, ommiting the verb "poder" ("podría", or "podrías" in a
colloquial context) is by large the preferred usage. Still, the form
preceded by the verb poder is not uncommon, as a way to emphasize
politeness.

Also, you can chose to ommit the conditional conjugation:

"¿Me da una servilleta?" The approximate English correspondance would
be: "Do you give me a napkin?", which would not be used in that
situation. Now, in Spanish, this option is at least as much used as
the conditional one, if not more. This one sounds closer to the
imperative form, but it's not it (what would be "Deme una
servilleta").

A slight and curious difference between the usage of the conditional
and non-conditional form for making a request:

"¿Me da una servilleta, por favor?" and "¿Me daría una servilleta?"
sound similarly polite. If you ommit "por favor" (please) in the first
case, you risk to sound a bit impolite (obviously, depending on your
general attitude and tone).

So, we can configure here an increasing scale of politenes:

1. Deme una servilleta. (imperative: mostly rude)
2. Deme una servilleta, por favor = ¿Me da una servilleta? (not
particularly kind, but OK, in the limit depending on you tone)
3. ¿Me da una servilleta, por favor? = ¿Me daría una servilleta?
(polite enough, most used)
4. ¿Me daría una servilleta, por favor? = ¿Podría darme una
servilleta? (particularly polite)
5. ¿Me podría dar una servilleta, por favor? (most polite)

Please take in account that not always the more polite the better,
specially in very colloquial situations where the excess of politeness
would sound affected or snob. To walk in the safe side, always use
options 3 or 4 and you'll do OK.

Now, instead of the distinction between polite and colloquial,
I would chose formal and informal, because you can be polite
or impolite in both contexts.

All the examples mentioned above are constructed in the formal style,
which means, supposing the formal "you" = "usted". To turn them into
the informal style, you only need to change the desinence to the
informal verbal inflexions:

deme -> dame;
da -> das;
daría -> darías;
podría -> podrías.

Please observe that the imperative form "deme una servilleta" would
sound rude unless there is a context justifying that usage, such a
very vertical relationship like in the army, or in an emergency when
you need to do things fast. However, the imperative will no be
necessarily impolite in a very informal context, typically at home,
provided the tone and attitude is agreeable.

______________________________________

Is: Puede me da una servilleta? -good grammar and where would it fit
in the 1-5 spectrum you listed?

I imagine that the size of a task might help determine if the more
polite Podría is used. Say, if the request was "to drive me to the
airport" rather than "give me a napkin". Me puede dar una servilleta?

__________________________________

As you've suspected, "¿Puede me da una servilleta?" is not correct,
while "¿Me puede dar una servilleta?" is. There's something curious
about it, because the conjugated form "puede" requires and infinitive
form -"dar"- and with infinitives the pronoun "me" needs to be
attached as a suffix, instead of being used as a preceding independent
word, as is the preference for most conjugated verbs -there are
exceptions such as the imperative forms, "deme", "dame". (By the way,
for most conjugated forms, the use of "me" as a suffix is not
incorrect but archaic: until the first decades of twentieth century,
"díjome" would have been as usual as "me dijo" -s/he told me- but it's
completely outdated now). However, you can use the pronoun "me"
separately provided that you put it before the conjugated verb, so
that you can say either: "me puede dar" or "puede darme", but not
"puede dar me". The place in the spectrum of politeness where I'd put
it is number two: the conditional seems to impact more in the
politeness effect than the use of the verb "poder".

Regarding the incidence of the task size in the level of politeness
needed, I agree with you, the bigger the effort you demand, the more
polite the request you need to make. Here is important to
differentiate the axis polite-impolite, from the axis formal-informal.
For example, if you ask your closest friend to drive you to the
airport, you need to be more polite than if you asked her to pass you
the salt -but not more formal. In such a case, it's frequent the
curious use of the negative phrasing for the request mentioned in
Scribe-ga's comment. "¿No me llevarías al aeropuerto?" with a slightly
pleading voice, like when saying "pleeeese" ;-) would be a very polite
request in an informal situation.