Unfortunately, we have a limitation on the length of our answers here (roughly 600 words), and Robert Browning's "The Pied Piper of Hamelin" is more than 2,100 words by itself. This makes your request an impossibility in this forum.
In general, the poem has both an erratic rhyme scheme and meter; that means that no two stanzas are alike, as you can tell simply by looking at them. There is clearly rhyme and rhythm throughout, but they are not consistent in this poem, much like a song or story which changes tempo or cadence at times.
Scansion marks are difficult to do here, so I'm substituting capital letters for the stressed syllables and keeping the unstressed syllable in lower case, as in the following:
To SEE/ the TOWNS/ folk SUFF/ er SO (this line is written in iambic tetrameter which would normally look like this: -/ -/ -/ -/ if you were scanning by hand)
Stanza III of the poem looks like this, then:
at LAST/ the PEO/ ple IN/ a BOdy (standard iambic pentameter)
TO the/ TOWN hall/ came FLOCK/ ing (trochaic, iambic, plus)
"‘tis CLEAR,"/ cried THEY,/ “our MAYOR’S/ a NODdy (iambic, plus)
and AS/ for our COR/ porA/ tion—SHOCK/ ing (iambic, anapest)
to THINK/ we BUY/ gowns LINED/ with ER/ mine (iambic, plus)
for DOLTS/ that CAN’T/ or WON’T/ deTER/ mine (iambic, plus)
what’s BEST/ to RID/ us OF/ our VER/ min (iambic tetrameter)
you HOPE/ beCAUSE/ you’re OLD/ and oBESE (iambic, anapest)
to FIND/ in the FURR/ y CI/ vic robe EASE (iambic, anapestic)
ROUSE up, sirs/ Give your BRAINS/ a RACK/ ing (dactyl, anapest, iamb, plus)
to FIND/ the RE/ medY/ we’re LACK/ ing (iambic tetrameter, plus)
or, SURE/ as FATE,/ we’ll SEND/ you PACK/ ing (iambic, plus)
at THIS/ the MAYOR/ and CORP/ porA/ tion (iambic, plus)
QUAKED with a / MIGHTy/ CONster/ NAtion (dactyl, iambic, plus)
Obviously there is no perfectly formed and adhered-to meter to this stanza, though it is primarily written in iambic tetrameter, often with a "plus"--a feminine foot (syllable) at the end of a line (such as the suffixes "ion" and "ing").
Looking at stanza VIII we find the same thing:
you SHOULD/ have HEARD/ the HAM/ elin PEO/ ple (iambic plus)
RINGing the/ BELLS till they/ ROCKED the/ STEEPle (dactyl/trochee)
GO cried the/ MAYor and/ GET LONG POLES (dactyl, spondees)
POKE out/ the NESTS/ and BLOCK/ up the HOLES (trochee, anapest)
conSULT/ with CAR/ penTERS/ and BUILD/ ers (iambic plus)
and LEAVE/ in our TOWN/ not EV/en a TRACE (iambic, anapest)
of the RATS/ when SUDden/ ly UP/ the FACE (anapest, iamb, other)
of the PIP/er PERKED/ in the MAR/ ketPLACE (anapest, iamb)
with a FIRST/ if you PLEASE/ my THOU/sand GUILD/ ers (anapest, iamb, plus)
The final stanza is just as erratic as the others--if not more so--probably for greater effect as he ends the story:
so WILLy/ let YOU/ and ME/ be WIPers
of SCORES/ OUT with/ ALL MEN/ esPECially/ PIPers
and WHETH/er they PIPE/ us FREE/ from RATS/ or from MICE
if we’ve PROM/ ised them OUGHT/ let us KEEP/ our PRO/ mise.
It's clear that Browning takes great liberty throughout the poem with the sound of this poem/ballad by using an erratic rhyme scheme and an uneven meter.
The result is a poem which reflects the rhythms of storytelling--sometimes we speak faster and more trippingly (the three-syllable feet, anapests and dactyls), sometimes we want to add emphasis and slow things down to be sure the audience gets it (the spondees), and sometimes we're just in a story-tellling rhythm (in this poem, an iambic rhythm).
It's not all you wanted, I know, but I hope this helps.