Is there a term for the phenomenon where the same word forms more than one part of speech?
In linguistics, a homonym is, in the strict sense, one of a group of words that share the same spelling and the same pronunciation but have different meanings
At http://www.thefreedictionary.com/duck, both the AHDEL and Collins claim that there are four English words 'duck'. They distinguish them by right-superscripts (which device is restricted to such analyses, of course).
The one they both choose to label duck {superscript3} is obviously not related to the other three - this is a case of convergent evolution, from different sources.
Although words 1, 2 and 4 are obviously etymologically related to each other (word 4 in a punning way), they are still considered to have diverged sufficiently to be classed as three further isoformal words (same spelling and pronunciation) - homonyms (strict definition).
However, if we delve deeper, and look, for instance, at AHDEL's treatment of duck {superscript3}, we see that it lists two (closely related) senses (admittedly one existing only in the plural form and the other almost invariably in the singular) - ONE the material and TWO clothing (usually trousers) made from that material. These senses are classed as not being separate words. Different senses of the same word are known as polysemes. An obvious example: to play football, you need a football.
Sadly, I have not come across a consensus on whether polysemy is a term that is allowed to be applied to isoformal / homographic orthographic words of different word-classes (eg house (n) and house (v); round (preposition) and round (adj) etc).
Oh, and in answer to the second question - an orthographic word is 'a meaningful (within the parameters of the language being used) string of letters bounded by spaces'. The term lexeme covers 'families' of 'the same word' , so man = man & men; go = go, goes ...
Edwin Ashworth
I've come across the term "intercategorial polysemy" used in lexicography and cognitive linguistics for the form of polysemy where the same orthographic word (and with the same etymology - not a homonym) is used in different word-class usages.
Thus bank (your money) and bank (where you bank it) but not bank (a steep natural incline).
Or bank (a steep natural incline) and bank (to border or protect with a ridge or embankment) but not bank (where you put your money).
This would make lecture (n) and lecture (v) say intercategorial polysemes.