أريد أن آكل خبزا وأشرب ماء.

Yes. أريدُ is the present tense (imperfect) meaning I want. In Modern Standard Arabic, using the present tense like this is the normal way to express wanting in general or right now.

• أريدُ = I want
• (More formal/longer option) أودّ أن... = I would like to...

Arabic verbs usually include the subject information. أريدُ already means I want because the verb form itself marks 1st person singular.
You can add أنا for emphasis or contrast:

• أريدُ أن... = I want to...
• أنا أريدُ أن... = I (specifically) want to...

أنْ is a particle that often corresponds to to (as in to eat, to drink) when one verb is followed by another verb in Arabic. It introduces a verb clause after verbs like want, like, prefer, can, etc.
So:

• أريدُ أنْ آكلَ = I want to eat
• أريدُ آكل (without أن) is not standard MSA.

After أنْ, the following verb is typically in the subjunctive (called المضارع المنصوب), which affects the ending vowel in fully-vowelled Arabic:

• أنْ آكلَ (subjunctive) instead of آكلُ (indicative)
• أنْ أشربَ instead of أشربُ
  In normal unvowelled writing, you often don’t see the difference, but it matters in careful pronunciation and grammar.

آ (alif madda) usually represents two hamzas becoming easier to write/pronounce: underlying أَأْكُلُ becomes آكُلُ.
Pronunciation is roughly /ʔaːkul/ (a hamza + long aa).
So آكل = I eat / I will eat (depending on context), and after أن it’s أن آكلَ = to eat.

و is simply and. It coordinates the second verb phrase with the first:

• أن آكل ... و(أن) أشرب ... = to eat … and (to) drink …

Both are possible in MSA, but the version without repeating أن is very common because the second verb is understood to be governed by the same أن:

• Common: أريد أن آكل خبزًا وأشرب ماءً
• Also correct (more explicit): أريد أن آكل خبزًا وأن أشرب ماءً

That ـا is often ألف التنوين (the “tanwīn alif”), used when a noun takes tanwīn fatḥ (ً) in the accusative and is indefinite. In fully vowelled form:

• خبزًا = bread (as a direct object, indefinite)
  The extra ا is a spelling convention that usually appears with ً at the end of many nouns.

Because it is the direct object (what you want to eat). In Arabic, direct objects take the accusative case (النصب):

• آكلُ خبزًا = I eat bread
  So in your sentence: أن آكلَ خبزًا = to eat bread.

In fully vowelled, careful MSA, it would normally be ماءً (accusative, indefinite) because it’s also a direct object of أشرب:

• أشربُ ماءً = I drink water
  In everyday unvowelled writing, tanwīn is often omitted, so you may just see ماء. If you add tanwīn, it’s placed on the final hamza: ماءً.

Because the sentence is expressing the general idea of having some bread and some water, not specific known items. If you mean the bread/water (specific), you’d use الـ:

• خبزًا / ماءً = (some) bread / (some) water
• الخبز / الماء = the bread / the water

In careful/formal pronunciation (like news or formal reading), you may pronounce them:

• خبزًا ≈ khubzan
• ماءً ≈ māʔan

But when pausing at the end of an utterance (or in much everyday speech), final case endings are often dropped:

• خبزًا may sound like khubzā (especially at pause)
• ماءً often sounds like māʔ at pause