The answer for professeur

Yes, this can be either a male or female. If the neologism « professeure » was used, definitely would refer to a female teacher, but « professeur » does not indicate the gender of the teacher. Articles are not used in this specific circumstance of defining occupation, but in other situations an article before the profession can indicate the person's gender, as covered in the lesson.

Of course, English has been moving to gender neutral occupational (and other personal) nouns for quite some years now, and the inability to specify a person's gender without further information is pretty much the norm in English too. 

Need the whole question to answer specifically. However, unless there was something in the sentence/context to otherwise restrict the answer to being a male teacher, the grammatically masculine noun « professeur » is invariable to 'actual gender', and  doesn't indicate this.  In the absence of a clarifying piece of information, « professeur » can be either male or female. 

One of the struggles of French for English speakers is to constantly remember that grammatical gender does not always indicate actual gender, as nouns can be invariable to actual gender.

Nor do the possessives eg « mon/ton/son professeur » help to identify 'actual gender'. The possessive article does indicate the grammatical gender of the following noun ( but only then when an invariable noun does NOT start with a vowel or h muet ). Context is needed to know the gender of the possessor/s, and with invariable nouns, to know the actual gender of the possession.

If you haven't come across them yet, you might want to check these further lessons on possessives (and others linked within them):

"Ma" becomes "mon" with feminine nouns starting with a vowel or mute h (French Possessive Adjectives)

Mon, ma, mes; ton, ta, tes; son, sa, ses = my; your; his / her in French (French possessive adjectives)

The question is Je suis professeur. Who is speaking? Then it says Leon , Marie or either of them. 

Thanks

Nicole

Just to add to Maarten's answer:

Whenever there is an article, you'll know: la professeur (female), le professeur (male). The noun itself is the same and offers no hint as to the gender.