advice on reentry permit

[immihelp]

Dear Sir / Madam,

I need some advice on reentry permit. I tried exploring different websites but none could actually give me a clear answer.
We as a family travelled to US in November 2009 on immigrant visa, got our green card after 2 weeks and travelled back to India in December 2009. We cannot remain in US for long since both our parents have a lot of health related probelms and needs medical care adn attention. Since the law demands we come back to US within 1 year from the date of previous visit, our second trip is planned in August this year. For the sake of our parents, we cannot stay more than two weeks again and we are planning to exit in 2 weeks.
I appreciate your reply on the following.

1) Is two weeks sufficient to apply for a reentry permit?
2) What can we do if it takes more than 2 weeks? Is there a way of expediting the process?
3) We are planning to come back to US every year, is renetry permit still needed?
4) Can anyone in US apply for reentry permit on our behalf so that we can get a biometric appointment faster?
Sorry for taking a lot of your time and thanks very much in advance for your help.

Kind regards

[immihelp]

If you are not planning to live in the US and don't live in the US, you risk losing your green card as you are given it to stay in the US.

Just by visiting the US once in a while is not enough.

1. No.
2. No.
3. Yes.
4. No.

Read https://www.immihelp.com/retain-greencard-useful-tips/ and http://www.immihelp.com/greencard/reentry-permit.html