Yes and no. I tend to skip the g if I talk fast (and I usually talk very, very fast), but were I to slow down, I'd pronounce it. Whether or not you do say it depends a lot on where you're from. Personally, I moved around a lot as a kid so my accent isn't based on one specific region.

I thought she bought northern newspapers...

"Several" implies a larger number than "some" to me. Either way, "flera" is a better Swedish translation for that word.