| | Re: long hair/mane
"a mane" is the specific name for longer hairs growing along the neck and on the head of an animal. You can talk, as you say, about a lion's mane, or eg a horse's mane.
"hair" is generally used for people - regardless whether it is on the head or other parts of the body - on your legs for example.
Most animals have "fur" all over their bodies, but in some cases "hair" is used - either as an alternative to "fur" (as with cats and dogs) or as the more usual term (as with horses). "Hair" is often used particularly to talk about individual hairs rather than the mane or the coat as a whole, and often when they are no longer attached to the animal :
There were dog hairs all over the sofa
Did you ever notice how much hair can collect on your comb after you have brushed your horse's mane and/or tail?
But notice how, in the last example, "hair" is not a synonym of "a mane" - it's the thing which the mane is made up of. Some more examples :
1."Pulling" means shortening the mane by removing the longest, straggling hairs to create a mane which is of one uniform length
2.Do not shampoo the mane and tail beforehand - it will make the hair too slippery and flyaway
3. A lion has a mass of longer hair on his head or neck which is called a mane
"mane" can also be used for people to indicate a very thick mass of hair : He had a shaggy mane of red hair.
So : a mane is not a synonym for hair, and the expression mane and longer hair(s) are therefore not interchangeable. A mane is seen as a single "thing", in the same way as a tail is seen as a single thing. Both a mane and a tail are made up of hair(s), but we would only use the word if we wanted to specify the individual hairs or the substance that the main/tail is composed of.
I hope that answers your questions...