Translation:He does not want to bike without his mother.
You already conjugated "willen" in this sentence, so you don't conjugate the second verb "fietsen". It's the same as in English where you say "He does not want to bike without his mother" instead of "He does not want bikes without his mother". When you have verb phrases like this, you only conjugate the first verb.
Well, I agree with your general statement, but I don't think that "niet" belongs in that position, rather it should be:
Hij wil niet zonder zijn moeder fietsen.
In Afrikaans, this particular word order is enforced by the STOMPI rule. I suppose Dutch is more lax with the word order, so the infinitive is not necessarily pushed all the way to the back?
Context indeed. Had it been "he does not want the bicycles", the translation would have been "Hij wil de fietsen niet" (you need the definite article + 'niet' behind the noun). Or "He does not want bicycles" (so, bicycles in general, not those specific ones) = "Hij wil geen fietsen" ('Geen' applies to the unspecified noun "fietsen"). And then "He does not want to bike" = Hij wil niet fietsen ('niet' because it applies to the verb)
True, because Duolingo is US-based. However, British equivalents (like petrol [gas], railway [railroad], flat [apartment], head teacher [principal] and grey [gray]) are accepted, although sometimes Duolingo does insist on "city" and "street" where British English might use "town" and "road".
I have noticed that Duolingo speaks American rather than English (even uses the US flag to denote English rather than the UK one). I can just about cope with talking about 'pants' instead of 'trousers' and 'underwear' instead of 'pants' - but 'bike' as a verb just sounds odd to me. Do Americans really never use the verb 'to cycle'?!
Soms zeggen wij Amerikanen "bicycle" as the verb.
I bicycle He/She/It bicycles You bicycle We bicycle They bicycle
I am bicycling He/She/It is bicycling You are bicycling We are bicycling They are bicycling.
So, you can see on one side of the Atlantic bi- was dropped in favor cycle, while on the other side of the Atlantic bike was adapted.