I'm definitely cool-toned (blue undertones) and a soft summer as well, but yes I can wear neutral based foundation, but can't wear warm-toned foundation at all. For the longest time, I wore L'Oreal True Match N2 and that was better than C2. I found the N2 helped neutralize the redness in my cheeks (rosacea). Then once the rosacea cleared up, I've since moved on to L'Oreal Infallible 415- Rose Ivory. It is absolute perfection for me as far as a color match goes. As for lipstick, I can only pull off shades with blue undertones, so mauves are awesome and fuchsia is my pink!
Meanwhile, my friend *appears* to have similar coloring to me (sometimes people think we're related) but she once stayed overnight and forgot her foundation so borrowed my C2. It looked like she'd smeared Calamine lotion all over her face!! She wears N2 instead. Turns out she is a Spring, not a Summer. Her natural hair color when it's not highlighted is very much like your own. And I've got to say that the green top you're wearing in pic 2 is her absolute favorite color and looks glorious on her, as it does on you! If you can wear peach that's another hint you may be a Spring.
My mom is also a Spring and your skin reminds me of hers. Also the top in pic 5 is one of her very best colors, but that color washes me out.
But then again I think you look great in the teal and blue tops so this is a tough call.
Despite being a summer, when I get highlights, my stylist uses a neutral color as anything too ashy looks absolutely horrible (as does anything too warm/golden). I am a natural blonde (towhead as a kid--darker blonde in adulthood). I also have lots of red in my hair (or did, before I started gaining some white hairs).
Not sure if that helps at all, just commiserating!