I wouldn't say longer, but certainly a more negative experience for the person waiting. (Except, of course, when we're talking about Kellner-style waiters - they're waiting on you, but that's not what you're talking about.)
If I'm waiting on you...then, I'm waiting on you to hurry up and get downstairs cuz we gotta go! If I'm waiting for you, then I'm not in as much of a rush for you to get down. I'll wait for you, take your time.
So, not necessarily a longer wait - just a more impatient wait.
"Wirst" is the future form of to be, and willst is a form of to want (wollen). Both imply a futuristic meaning. The difference lies in the intention behind the future plan one expresses with those verbs: - Ich will die Welt bereisen (I want to travel the world) v. -Ich werde die Welt bereisen (I will travel the world) -> the latter is certainly stronger in respect to the actual intention to act on the plan, the former is rather a wish than a concrete plan - same holds for wird/will
It's not accusative solely due to the preposition 'auf'. Whether auf puts the noun in dative or accusative depends on whether direction (motion) or location is involved in the action. Here, though, auf is part of the phrase "auf etw/jmdn warten" meaning "to wait for st/sb": the noun in this phrase will always be in accusative. So, you'll just have to know....that sometimes it's the preposition and sometimes it's the phrase that determines the case.
werden -- to become, to turn. Used like english 'will' in building the future tense (that's done in this duolingo example). Also used like english 'is' in building passive tense: werden: ich werde; du wirst; er/sie/es wird; wir werden; ihr werdet; sie/Sie werden
wollen -- to want. This is a modal verb, which is different from english. wollen: ich will; du willst; er/sie/es will; wir wollen; ihr wollt; sie/Sie wollen
Certain verbs and prepositions team up, and this team determines a case for the objects of the verb-preposition phrase. warten-auf determines the accusative case. kreisen-um determines accusative. But, teilnehmen-an determines dative.
Ich warte auf dich -- I'm waiting for you. (accusative)
Der Satellit kreist um die Erde -- The satellite orbits the earth. (accusative)
Ich nehme an einem Wettkampf teil -- I take part in a competition. (dative)
Nope. The "auxiliary verb" werden (used to form the future tense) sends the infinitive warten to the end of the clause. This is the same as if you used a "modal verb".
Wirst du auf mich warten? -- Will you wait for me?
Könntest du auf mich warten? -- Could you wait for me?
Solltest du auf mich warten? -- Should you wait for me?
And, were you to use the auxiliary verb haben (to form the past perfect tense), you'd put the "past participle" (gewartet -- waited) at the end of the clause:
Hast du auf mich gewartet? -- Have you waited for me? / Did you wait for me?
warten is the verb in its infinitive form. Here, it's part of the verb phrase "auf jemanden warten", which means "to wait for somebody".
So, "wirst du auf mich warten"... "auf" comes before "mich" because that's the phrase: "auf jemanden warten".
"Warte auf mich!" -- "Wait for me!"
"Ich werde auf ihn warten" -- "I'll wait for him"
I've never heard anyone say "aufwarten", but apparently it's a part of the phrase "jmdm. mit etw. aufwarten" meaning "to offer/serve sb. [with] sth.", and an obsolete meaning is "to wait on" in the sense of being a waiter at a restaurant. You'd rather say "bedienen" here, though.
I can't think of an example when an english speaker would say that. There's 'wait on' me, in the sense of a waiter at a restaurant or I'm running late, and there's 'wait for' me, in the sense of you're being impatient or "Wait for me!" because you're going too fast and I want to catch up. Never "wait me", though.