HPA use a nice flavour profile system made up of the four flavour characteristics, fruity (whether it be citrus or melon or stone fruits etc), Resiny (I like to think of these as earthy and woody flavours like rosemary and pine), Spicy (the pepper warmth that noble varieties are jam packed with) and finally Floral.
Some hops are loved for having complex characteristics like motueka (B sazz) because of its spicy and fruity qualities.
This type of thinking has lead me to some random hop combos that have paid off. I regularly pair noble varieties with fruity american hops to give a more complex spicy flavour to my american style beers.
Oddly enough I entered an ESB into a comp last year, which I paired Hallertau and EKG. The feedback from the judges was and I quote "did you just re-bottle Fullers?" I couldn't have been more happy.
Your questions about no chill vs chill are more complicated. I used to always chill but after my son was born I have sliced off non essentials from my brew day. I now save a stack of time cleaning and fussing about getting to pitching temp but it does carry a new set of challenges. I ran a series of test brews where I only hopped in the cube and then on other I didn't hop in the cube or dry hop at all.
I have found that the lack of chilling does kill the big aroma benefits of late kettle hopping, with my non cube hopped beers lacked the hoppy aroma I would have liked. That being said, it doesn't hold me back or prevent me from getting the desired result. If I'm brewing a style that doesn't need late additions, I brew as normal. If it does need late additions, I replace my 15min addition to be in the cube and anything under goes in dry. It's does mean I have to plan for the no chill, adjusting addition times and recalculating IBU's, but the beer hasn't suffered. I had 3 guys consisting of 2 other home brewers over on the weekend. I tapped a keg of american brown ale and it went down really well, they couldn't get enough of it! And funnily enough it was a saaz, citra and cascade combo.
The hardest part about no chill brewing and putting together hop combos is high AA hops, they can be tricky to get the aroma and flavour without a huge bitter kick. But as I said, it just takes planning and readjusting recipes to ensure you still get the desired effect.
Frankly I struggle to believe I'll ever use my chiller again.