: 1.I noticed that in LOTR most of the characters' appearance
: is described (for example,the colour of their hair and
: eyes), but there is no exact description of Frodo. What could
: be the reason?

There is a partial description of him, at least, in what Gandalf told Butterburr to look out for. Whether or why Tolkien would not distinguish between Frodo and other hobbits in general is a matter for speculation, I would say.

Perhaps he wanted Frodo to be non-descript, a sort of "Every Hobbit" character.

: 2.Everybody in the book smokes pipe-weed (Gandalf,Aragorn,
: Merry,Pippin,Sam,etc...),but it is never mentioned in the whole
: book that Frodo smoked.
:
: And,when the hobbits and Gandalf meet Saruman on their way back
: to the Shire,Saruman says:"...You would not give a pipeful to a
: beggar,would you?"
: And Frodo replies:"I would,if I had any." (ROTK p.962)
: So did Frodo smoke or not?

I cannot remember any mention of Frodo having smoked. There is no reason to assume he did (or, rather, that ALL hobbits did). He may simply have been a non-smoker. Of course, Frodo was seldom if ever in a situation would smoking would have added something to his personal story. Gandalf smokes to think, and Aragorn and the others smoke to relax after a good meal, etc.

The idea that smoking tobacco (or a similar substance) was addictive was not around when the story was written. So I don't believe Tolkien would have envisioned any of the characters NEEDING to smoke. He himself smoked, of course, and I'm sure that like many pipe smokers he found great comfort in it. He was fortunate enough to be spared some of the afflictions pipe smokers suffer -- such as mouth cancer.

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Parma Endorion: Essays On Middle-earth, Revised Edition