In theory each verb in Irish has two forms for each tense, the independent form and the dependent form. The independent form is used in normal statements; the dependent form is used after most pre-verbal particles, such as 'an' used for questions, 'ní' used to make a verb negative, 'nach' to form negative questions, etc. So the verb 'bí' in the simple present tense has 'tá' as its independent form and 'fuil' as its dependent form. You'll never see 'fuil' used by itself though. All the pre-verbal particles cause some kind of mutation, so in a question you'll have 'an bhfuil', in a negative question 'nach bhfuil' ('an' and 'nach' cause a mutation called eclipsis, whereby 'f' becomes 'bh'), in the negative 'níl' ('ní' causes a different mutation, called lenition, whereby 'f' becomes 'fh', and since 'fh' is always silent 'ní fhuil' is pronounced 'níl' and written accordingly). Fortunately, however, 'bí' is exceptionally irregular (but also indispensable, I'm afraid you'll just have to learn it), but in the vast majority of verbs the independent and dependent forms are actually identical. Only about four or five verbs have an irregular dependent form, and only in one or two tenses at that. In fact, you'll be pleased to know that Irish only has 11 irregular verbs, and some of those are only very slightly irregular. I'm not sure what you mean by plural, singular and possessive variations of the verb 'to eat', I suspect you're misunderstanding something. If you give me an example I'll be able to explain it to you.