Imagine instead of "pita" it is "Barack Obama." Barack Obama is married to Michelle Obama—not Michelle Obami (even though she is female). Obama cannot change to Obami :) Likewise, we would not say "Barack Obame ko khaana hai." We would say "...Obama ko...." "Obama" will never change, despite the fact that his name ends in /a/.
Pita is like Obama :) Even though it ends in /a/, it follows the rules for words that end in a consonant.
मैं ओबामा जी से पयार करता हूँ।
Yes (though be warned: there are multiple ways to say "have to").
verb root + na --> the infinitive. In a very very technical nerdy geeky pedantic and probably irrelevant to you sense :) , the infinitive is not exactly equivalent to verb root + na. So the super nerdy thing to say is that it's the infinitive here. But forget I said it!
I think it was the Rocket Hindi course that had quite a good module on this, but it's about degrees of need - English has 'I should eat', 'I have to eat', 'I must eat', 'I need to eat', 'It's essential that I eat' etc that carry varying degrees of urgency. Hindi has the same. It's a bit arbitrary but I'd say that 'needs' (which I think would be expressed using 'zarurat' in Hindi) is a step up the urgency scale from 'has to'.
See Sam362597's comment, directly above.
The word "must" in English usually carries a greater degree of urgency than is implied by the Hindi sentence. I realize that perhaps it does not sound that way in your dialect of English. But the bigger picture is that eventually in Hindi learning one will see different ways of expressing "compulsion," and it's useful to start distinguishing in how we translate.
The Hindi sentence in this example is more like a strong expectation or suggestion.
This is just a curiosity, but the distinction between "have to" and "must" is slightly more detailed than solely a question of degree. From the British Council website:
Have to shows us that the obligation comes from somebody else. It’s a law or a rule and the speaker can’t change it: Do you have to wear a uniform at your school? Must shows us that the obligation comes from the speaker. It isn’t a law or a rule: I must call my dad tonight.
The British Council is just a language teacher of one dialect of English, not a language authority, like the Académie Française, or even a style guide. If you never knew the difference, then very likely there is no difference in your dialect of English, ad there is none in mine. Since English has no language authority, there is no source one can turn to to say the English spoken where you live is in some way sub-standard.
Native English speaker here and I'm rather doubtful of the British Council website I'm afraid - certainly no more than 50 years ago 'may' would surely have been the main acceptable modal verb for asking permission and 'can' would have been used for ability only; just twenty years ago I was still regularly told in school that 'can' was incorrect to ask permission although it was coming into common use.
Even if 'have to' were to show that obligation comes from someone else and 'must' from the speaker, I'm still fairly certain that firstly, 'must' and 'need to' carry different connotations again so Sam362597's comment about 'ज़रूरत' doesn't necessarily apply to 'must'; secondly I don't recall there being such a hard rule that the Hindi (inf)+होना doesn't always signify an external compulsion, so while there may be a technical distinction between 'have to' and 'must' in English, i'm not convinced that '(inf)+होना' wouldn't be able to apply to them both in English, just as I've read elsewhere that 'चाहिए' can apply to both as well.
As an example from another language, 'Let's go' and 'We go' have two very different meanings in English, but in Italian, 'Andiamo' covers them both equally well.
Incidentally, I've also read 'मुझे खाना है' translated elsewhere as 'I want to eat' which definitely signifies no external obligation!
I reckon that there's more nuance to all of these expressions than Duolingo is allowing for here and 'must' should be accepted.