Firecrackers are enjoyable, no doubt, but they are also dangerous things to play with, for they can easily cause fire, and they are dangerous things to make.

They should therefore be made by adult only, and carefully.

"no doubt" is an adverb or adverbial?

"only" is modifying the verb "made" or "adult"?

I suppose it's an adverbial-- an idiomatic verbless comment clause (from the expanded 'I have no doubt'?)

'Made by adults only' = 'made only by adults' = 'only made by adults'. What do you think, Hanuman?
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Very nice!

Now I got. It is an adverb, modifying the verb "made".

Sir, one more question, "Only" trouble me a lot.

Somewhere , I have read that only just come before the word it modify.

"only" functions as an adjective and an adverb both.

How to distinguish them?

Your are master in English so you can catch it very easily, but for me it is rather difficult.

Well, we have just seen that 'only' need not be solely a premodifier. As with any modifier, you must find the referrent to determine if it is an adverb or adjective:

'He is an only child.' -- adjective, eh?

'He only pretends to be happy.' -- adverb, of course.