Yes, soup is eaten, not drunk in Russian.

Yes. If you use a spoon, then you definitely should use «есть».

However, here's a news item 'Drinking soup is convenient', about a innovative kitchenware that doesn't require a spoon: http://tutdesign.ru/cats/object/975-pit-sup-yeto-udobno.html — it uses the word «пить». But it's not how we usually consume soups.

Where is soup drunken in general speech?

The same: "Моя сестра ест суп."

(At least I think so. Context should tell you which one is meant, but it doesn't always do that. Some differences are not important to some languages.)

it's the same,since there are no definite and indefinite articles in russian

Ест is singular, едят is plural:

• Она ест. ‘She eats.’
• Ма́ма ест. ‘Mum eats.’
• Они́ едя́т. ‘They eat.’
• Де́ти едя́т. ‘[The] children eat.’

Both are 3rd person forms, meaning they are used when talking about people who don’t participate in the conversation.

All in all, there are 6 forms of the Russian verb for each tense. There are also 1st person forms, used when the speaker does an action (я ем ‘I eat’, мы едим ‘we eat’), and 2nd person forms, used when the listener does an action (ты ешь ‘you eat’ [singular informal], вы еди́те ‘you eat [polite and plural]).

Есть is an irregular verb: the form я ем is irregular (I think only я дам ‘I will give’ has the same ending in the 1st person singular). Most other verbs have 1st person singular in -у or -ю.

'Супа' is genitive singular, whereas what is required here is accusative singular (which is the same as nominative singular for inanimate masculine nouns like 'суп').

There is no у at the beginning of the sentence, also sister is in nominative, and it is ест (eat for he/she), not есть (meaning having)