3) b)
38国 is also acceptable.
As for か/ヶ, it's said that this counter is used for the ones that CAN mean an ordinal number such like 月, 条. For instanse, 三条 can refer to the third article, whereas 三ヶ条 only means three articles. This rule can't be applied to all counters, though.
4) a)
It more likely means "at least eating". Purely grammatically, it sould be 食事を食べる(とき)くらい for that meaning, but the writer would use it as the same sense as 食事くらいゆっくりしよう.