Can I travel to US on H4 visa in June 2014 when I have H1B approved on May 2014 which is effective from Oct 2014?

You may travel as stated, however, in all pending issues it would be reasonable to seek assistance from the counsel of record who is familiar with...

USCIS rejected H-1B petition saying "different Service Center had jurisdiction over the place of employment" what next ?

Speak with the immigration attorney you are working with.

Spouse visa outside US- DS260

Because the government asked you to. Maybe you went to a school that is a terrorist training center.

Need a proxy for my sister's stay with me?

This really isnt an immigration question, however, if a worse case scenario happens and you need to bring your sister to the hospital lets say,...

How do we proceed to get my daughters fiances legal in the US? he has been here 10 years and is 21. How expensive is it?

If he had a greencard, then he hasnt been here illegally. You don't lose your privileges just because you lost your card or it expired. He should...

Should I notify an attorney

You do not provide any context to this question, so it's difficult to understand. Is this out of the blue? Are you from the DR? Is it a scam?

A good rule of thumb that I tell my clients is to stay out as long as you stayed in. If he applies again so soon after staying for 6 months, there...

I recently became an US citizen. My only brother lives in a country where I came from.

You are correct, 11 years sounds about right, it could be even longer. There is no way to shorten it through your petition.

My husband wants to become a permanent resident in Canada.

Sorry, we are US Immigration Lawyers, you should speak with a Canadian Immigration Lawyer for advice.

H1B Transfer - 3 business days gap between employers

You'll be fine, just dont leave the country.