No, FF isn't recommended in any carrier. Some manufacturers will tell you you can but it's really not good for LO's hips. It wouldn't hurt to do it every now and then BUT if you show LO the option, she'll probably want it all the time. As she gets a bit older, you can probably adjust the wrap a bit to let her see better. By about 8 months, my LO would sort of turn sideways with one arm out and that allowed her to see plenty.
I couldn't use a stretchy wrap at all, it was just too warm for me even in winter. As your LO is getting older now, it might be time to think about moving on to either a woven wrap or another type of carrier as I would imagine a stretchy won't be supportive enough for too much longer. I used a mei tai which was nice as although it was a fairly thick woven material for the back panel, you get gaps around the sides for a bit of a breeze. It was the same with a soft structured carrier e.g. R&R, Connecta, Ergo. My favourite was a woven wrap though - even though you have as many layers as a stretchy, they come in loads of different fabrics so you can go for a cooler one. Mine is cotton and is nice and cool, plus as they're more supportive than a stretchy you can do loads of different carries, some with only one layer of fabric across LO's back.
Do you have a sling library near you? It might be worth going along for a test drive.