Font (noun) : an assortment or set of type or characters all of one style and sometimes one size.
A font is a set of printable or displayable text characters in a specific style and size. The type design for a set of fonts is the typeface and variations of this design form the typeface family. Thus, Helvetica is a typeface family, Helvetica italic is a typeface, and Helvetica italic 10-point is a font.source
It's also used to define the name of the digital file used to render the style of a text on computers. In that case it should be called font files.
Is it still a font if I expand it to be a path?
But it's a vectorized text built on the font you used. If you vectorize Futura bold 10pts, it's still Futura bold 10pts, the same way as it would still be it once printed; it can be measured and identified. Printed fonts are technically not active or editable but they don't lose their name or family because of this.
You could always call the Futura Bold 10 pts letter "A" vectorized "the A glyph from the Futural bold font" or simply cut it short to a "Futura Bold letter A". The term glyph is more commonly used by typographers to specify each set of character to build the font but in design and to be understood by clients (and 99% of the population), it's usually simply called a letter/character. The term glyph refers more often to the construction of the font, the term letter to its usage and both should be right since it is still a glyph and a letter/character with a specific style.
Is it still a font if I expand it to be a path with no stroke or fill?
This is relative.
As long as the shape of the font is visible, it's still the same font, used with a different visual and artistic style.
If it's just a path that makes the text lose its characteristics that can make it identifiable with a precise font or typeface then it's just a vector with a letter shape.
If I draw a shape that resembles the letter "A" only using the pen
tool (no type tool) then is that A a font?
The letter "A" became a vector graphic with the shape of a letter! Technically not a font unless you decide to create a font file with that style. It's like handwriting in that case.
Are these Granny Smith apples?
Yes. It's a basket of apples named Granny Smith.
If I take one apple out of the basket or off the tree it grew in, is it still a Granny Smith apple?
If I turn them into jam, will they still be Granny Smith apples?
Yes. Simply not "fresh" apples anymore but still easy to identify from other jams.
If I peel it and cut it into quarters, is it still a Granny Smith apple?
Yes. They're pieces of apples but you could still call them Granny Smith. Or you could call them 1/4 slices of hybrid fruit from Malus domestica × M. sylvestris, that works too...
If I add chemical to change their property and they become blue, magically change their molecular structure and DNA, and become not comestible, are they still Granny Smith apples?
No. It's your creation and you can name it as you want.