First, "rate poverty" is incorrect. You should either say "poverty rate" or "amount of poverty". I've fixed this in my quotations below.
On to your question:
- Regardless of how developed it is, every country has a certain amount of poverty.
This sounds natural.
- Every country has a certain amount of poverty, regardless of how developed it is.
Also natural. The "it is" is necessary.
- Regardless of the country, there is a certain amount of poverty in every country.
This is redundant. "Regardless of the country" means the same thing as "in every country". Drop "Regardless of the country" from the sentence. You can also say "any country" instead of "every country".
- Regardless of their race, religion or sex everyone deserves to be treated respectfully.
I fixed the tense of "treat". This sentence is almost natural, but could use a comma after "sex". It would be more common to put "everyone deserves to be treated respectfully" first in the sentence, but either order works.
- Regardless of how busy you are, everyone needs a good night's sleep.
You can say that you had a good nap or a good rest, but "a good sleep" doesn't work. The normal way to say this is "a good night's sleep".
The rest of the sentence is almost natural. In casual speech you could get away with it. It would be better to make the subjects agree:
Regardless of how busy they are, everyone needs a good night's sleep.
Regardless of how busy you are, you still need a good night's sleep.
[This space intentionally left blank.]
- You cannot get on this web site but it is regardless of your age or sex. It is based on the country that is associated with your IP address.
The second sentence needs some work. I put one suggestion in my quote. Other options include "the country that your IP address comes from" or "the country where your IP address is located". You could also change "It" to something more specific.
The first sentence is almost natural. Again, you could probably get away with it in casual speech. It would be better to say:
You cannot get on this web site, but that has nothing to do with your age or sex.
Your inability to get on this web site has nothing to do with your age or sex.
That has better grammar, but it also sounds more formal.
I agree with Colleen's answer about the order of the sentences.