Answer:
Extracting the letters "ABCDEFG" from the clues and interpreting as if they were musical notes, we get fragments of the melodies of the song being clued.
First group
Theme is CALIFORNIA
1. No oFFEnsE to olD moms or pops, I woulD think I'm too younG to know your Folk rECorD.
"California Dreamin'", by The Mamas & The Papas. It's an old folk record
FFEED DGFECD -> "California Dreamin' on such a winter's day".
2. With lots oF Fun FluFFy pillows, viD shows Flirty Girl with mAuvish hAir in hot outFits.
"California Gurls", by Katy Perry. The video shows her with violet hair and fluffy clouds as pillows.
FFFFF DFGAAF -> "California girls, we're unforgettable".
3. No Frills inn Full oF GloomFul FlunkiEs, EvEry Exit oDDly lost, two Dons' rowDy olD roCk musiC hit.
"Hotel California", by Eagles. The song is about a spooky hotel (inn) that you can never leave. An old rock music hit by a band with two Dons (Felder and Henley)
FFFGFFE EEEDD DDDCC -> "The hotel California, such a lovely place, such a lovely face".
SECOND GROUP
Theme is NEW YORK
1. GrAmmy, to GiAnt rAp stAr's AmAzinG rhythmiC hit with womAn, who sinGs AlonG Chorus pArts.
"Empire State of Mind", by Jay-Z and Alicia Keys. The chorus prominently features "New York", Jay-Z is a rap star, Keys sings the chorus, and the song won a couple of Grammy Awards.
GA GAAAAAGCA GAGCA -> "New York, Concrete jungle where dreams are made of, there's nothing you can do".
2. YounG Girl sinGinG own sonGs, GiGGlinG with Glossy lips, prouD to sport BlonD BAnGs.
"Welcome to New York", by Taylor Swift?. She fits the description of blonde, giggling young songwriter.
GGGGG GGGGG DBDBAG -> "Welcome to New York, welcome to New York, it's been waiting for you"
3. JoEl on kEys, wonDrous ChorDs with purE tonEs, no DisCorD EvEr, mooDy lyriCs not DisCo musiC.
"New York State of Mind", by Billy Joel. Joel is a talented pianist.
EE DCDEE DCDEE DCDCC -> "Some folks like to get away, take a holiday from the neighborhood".
CHALLENGE GROUP
1. ThEy'rE shirtlEss in thEir viDs, is this rED hot, or just Chilly?
"Californication", by the Red Hot Chili Peppers. Obviously in the California group.
EEEED ED C -> "Dream of Californication".
2. First, sEt Forth to DisCuss rumors.
"New York, New York", by Frank Sinatra (and others). "Set forth to discuss rumors" is synonymous with the first line of the song, "Start spreadin' the news".
F EFDC -> "Start spreadin' the news".
3. SinGinG, in hArmony, it's roCk n' roll, mEloDious, voCAlly oriGinAl, know it By now?
"California Girls", by the Beach Boys. They played rock 'n' roll and were known by their vocal harmonies.
GG A C ED CAGA B -> "I wish they all could be California girls".