Ještě chvíli budu odpočívat doma.

Because odpočívat is an imperfective verb, and in Czech the future of imperfective verbs is usually made with být in the future + infinitive.

• budu odpočívat = I will be resting / I will rest
• literally: I will rest

This is different from perfective verbs, which often form the future with a single present-looking form.

Ještě chvíli means for a little while longer, a bit longer, or for another moment.

• ještě = still, yet, more, another
• chvíli = a short while, a moment

Together they express continuation for a short time: the speaker will keep resting a little longer.

Because chvíli is the accusative singular of chvíle.

In this sentence, the accusative is used to express duration of time:

• čekám hodinu = I am waiting for an hour
• spal celou noc = he slept all night
• ještě chvíli = for a little while longer

So chvíli is not the object in the English sense, but it is in the accusative because Czech often uses the accusative for how long something lasts.

Because doma means at home, while domů means homeward / to home.

• odpočívat doma = to rest at home
• jdu domů = I am going home

Here there is no movement toward home. The speaker is located there, so doma is correct.

They are related but differ in aspect.

• odpočívat = imperfective
  Focuses on the process, duration, or repeated activity of resting.
• odpočinout si = perfective
  Focuses on completing the rest or taking a rest as a whole.

In this sentence, budu odpočívat fits well because the speaker is talking about spending some more time resting.

Compare:

• Ještě chvíli budu odpočívat. = I’ll keep resting a little longer.
• Odpočinu si a pak půjdu pryč. = I’ll get some rest and then I’ll leave.

It can mean either, depending on context.

Czech does not always make the same sharp distinction English makes between will rest and will be resting. The form budu odpočívat often suggests an ongoing activity, so I’ll be resting can be a very natural translation, but I’ll rest may also work.

Because of ještě chvíli, the idea of continuing for some time is strong, so I’ll rest a bit longer or I’ll be resting a bit longer both fit well.

Yes. Czech word order is flexible, and changing it usually changes emphasis, not the basic meaning.

Original:

• Ještě chvíli budu odpočívat doma.

Possible alternatives:

• Budu ještě chvíli odpočívat doma.
• Doma budu ještě chvíli odpočívat.
• Ještě chvíli doma budu odpočívat.

The original sounds natural and neutral. Putting doma earlier can emphasize at home, and putting budu earlier can make the sentence sound a little more straightforward.

No. Ještě has several common uses, and the exact translation depends on context.

It can mean:

• still: Ještě spí. = He is still sleeping.
• yet: Ještě ne. = Not yet.
• more / another: Ještě kávu? = More coffee?
• further continuation: Ještě chvíli = a little while longer

So in this sentence, translating ještě as still by itself would sound incomplete in English. The phrase ještě chvíli works as a unit.

Yes, that is possible and understandable.

However, ještě chvíli often sounds most natural before the verb phrase or near the beginning of the sentence when it sets the time-span of the whole action:

• Ještě chvíli budu odpočívat doma.
• Budu ještě chvíli odpočívat doma.

Putting it later is not wrong, but it may sound slightly less neutral depending on context.

A few things may stand out for English speakers:

• ještě: the j sounds like English y in yes
• šť in ještě is a soft consonant cluster; pronounce it smoothly, not as a hard st
• ch in chvíli is like the ch in German Bach or Scottish loch, not like English ch in chair
• ř does not appear in this sentence, so that famous Czech sound is not a problem here
• stress in Czech usually falls on the first syllable of each word:
  • JEŠ-tě
  • CHVÍ-li
  • BU-du
  • od-po-ČÍ-vat
  • DO-ma

Also, in normal speech, the sentence flows quite smoothly, with the main emphasis often falling on ještě chvíli or doma, depending on what the speaker wants to highlight.

Yes, it can, but only if the context supports that reading.

By itself, doma simply states location: at home. But in conversation, word order and stress can make it contrastive:

• Ještě chvíli budu odpočívat doma. = I’ll rest at home a bit longer.
• If stressed strongly: ... doma could imply at home, not somewhere else.

Without special emphasis, though, it is just a normal statement of where the resting will happen.