Do these sentences have the same meaning? Are they grammatically correct?

1) Most butterflies don't live quite as long as bees - Bees live nearly as long as butterflies I think you missed  a few words in the second sentence.  I've added in my guess. These sentences do not have the same meaning. The first says butterflies live less for less time than bees. The second says bees live for less time than butterflies. The phrase "nearly as long as" implies "but less than".
2) Snakes are much less dangerous than people think - Snakes are not nearly as dangerous as people think Yes, these have the same meaning in this context. Yes, they are both grammatically correct. Usually "much less" would put you further away than "not nearly" but in this context of dangerous snakes they convey the same thing.  As an example, 15 is not nearly as much as 20 whereas 12 is much less than 20. 
3) A spider's silk is five times stronger than steel - Steel is nowhere near as strong as a spider's silk is These also have generally the same meaning. Five times is an exact amount and conveys the magnitude of the difference.  The description "nowhere near" does not give the same sense of comparison and it comes across as a little clumsy. If the difference was only twice as strong could you still say nowhere near? The grammer on the 2nd is incorrect; the "is" at the end is not correct.  In my opinion, it would be slightly better to not say "a spider's silk" but rather to say "spider silk".  
4) Lions aren't quite as big as tigers - Tigers are slightly bigger than lions These have essentially the same meaning. You would write one or the other to convey a slightly nuanced difference. The grammar is correct. 
5) Bears live half as long as elephants - Elephants live twice as long as bears These have the same meaning for the comparison. The second is slightly more pleasing to the ear. The first is a little awkward. 
6) A blue whale's heart is the same size as a small car - A blue whale's heart is as big as a small car These have the same meaning.  The second phrasing gives more emphasis to understand how big the heart is.  Also, when you say "the same size", it can imply something that was measured. If you were to say "is about the same size" it conveys the comparison without implying a measurement.