Both are correct. The first form ("¿Quiere comer algo?") is used with unknown people, or as a respectful form with elders. It is assumed you are talking to 'usted': "¿Quiere usted comer algo?" The second one ("¿Quieres comer algo?") is for friends, used as a casual form. Here you're talking to 'tú': "¿Quieres tú comer algo?" (although is very unusual to say it using 'tú')

I agree with Manu. ¿Quiere comer algo? (formal) ¿Quieres comer algo? (informal) But I would add also a third form: ¿Querés comer algo? (informal, used in South América)

¿Quieres comer (algo)? ¿Te apetece comer (algo)? ¿Tienes hambre?

Hello i am Jenny I saw your profile today at italki.com so i decided to write to you, here is my email([email protected]) so that I will send my picture,

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