I was convinced it should be plural because the accusative singular would be "golarkę". Turns out that "potrzebuję" takes the genitive (see https://en.wiktionary.org/wiki/potrzebowa%C4%87) so "golarki" is genitive singular rather than accusative plural. But unless I've missed some explanation, this wasn't made terribly obvious here.
Yes, the Polish verb "potrzebować" requires the genitive case of the following noun.
It is good to know the Polish verb does not go with every possible noun though. It is closer in meaning to the verb "to yearn for" (pragnąć) and refers to something you really cannot live without like water, air, happiness, money, and god, to name a few:
Potrzebuję wody/ powietrza/ szczęścia/ pieniędzy/ boga (Genitive - Dopełniacz)
Obviously, you can live your life without shaving, and a razor (maszynka do golenia). For needs of things (and... people) which make your life easier and more convenient,
rather different Polish construction, in passive voice, is used:
I need a razor - Potrzebna mi maszynka do golenia/golarka (Nominative - Mianownik)
I need you/a new employee - Jesteś mi potrzebny/ Potrzebny mi nowy pracownik
I need a shave/ I need to shave - Muszę się ogolić
I need a haircut/ I need to get a haircut - Muszę się ostrzyc
"golarek" (declension here)
You can also find the name "maszynka do golenia" (little machine for shaving) - although it's a lot longer, it's in normal use and for example I'd be more likely to use that than 'golarka'. "Maszynka" itself could probably be understood to mean the same, although that's only 'probably'.
No no no. That would be like "I would like I drink coffee". It wouldn't make sense.
Well, with words you know, you could write "Chciałbym pić kawę", which would be "I would like to drink coffee" - but it'd sound as... if you wanted to spend your life drinking coffee? as if you wanted to drink coffee for a living?
You should use one of the perfective equivalents here. So either you have "Chciałbym wypić kawę" (I'd like to drink the whole cup/mug/whatever of coffee) or "Chciałbym napić się kawy" (with Genitive), as in "I would like to drink (a bit/some) coffee).