"Tengo que ir a comprar un coche."
Translation:I have to go buy a car.
It's difficult to directly translate a language. In Spanish, we constantly use <<tengo que ...>>> to just state things that we have to do. If I'm like "I have to go buy/must buy a car" I'd say <<tengo que ir a comprar[me] un carro/coche>> I naturally make it reflexive too, I don't know why. It just sounds like Im doing the act of buying like for a job or because that's what I do or something like that and not because I'm buying it for myself.
Not strictly so, although in this sentence you do need the "directional a". 'Ir' is followed by an 'a' if you are going to a physical location, and in the idiom "ir+a" meaning "to be going to/will" (as in voy a leer, I will read), and this is the majority of cases. However you can have "ir" without "a", eg "van cada día" = "they go every day" or "voy con mí esposa" = "I go with my wife".
I think of it as ir+a = go to, ir=go.
I don't agree with you -- we must have learned English in different places........
I must pay taxes. I have to pay taxes. --- Same sentence where I grew up.
I must work to pay bills. I have to work to pay bills.
I must go to school to pass my classes. I have to go to school to pass my classes.
Duo is probably conditioning you to use the sentences in the mentality of a Spanish speaker. For me (a native Spanish speaker), it sounds 100%, even though I do not know why. Just let them guide you. I do Spanish for fun and have not seen any problem thus far.
Remember that Duo goes by La Real Academia Española, la RAE, which is the official dictionary of the Spanish language. And, coche, although it means cradle for me as a Cuban, is the official way to say car. Maybe carro is a word made by the English word car. Who knows. But the word recognized by the RAE as the official term is coche, even thought they recognize carro as a word that equally describes a car. Duo should accept both.