Lost passport with US visa (Non Immigrant) in USA , can I get my US Visa replaced in USA?

Unfortunately, no.

From the State Department:

If you are a foreign citizen temporarily in the United States, and you lose your U.S. visa, you can remain for the duration of your authorized stay, as shown on your admission stamp or paper Form I-94, Arrival/Departure Record.

So at least you can stay, get a new passport, and still depart on that new passport, but when you next leave the country you'll need to replace the visa to be allowed back in.

Note that on that page, there are several steps you should follow as well, in terms of contacting the police, your embassy and that you'll need copies of these discussions when applying for the replacement visa:

For replacement of a visa, you must apply in person at a U.S. Embassy or Consulate abroad. When applying for the replacement of a visa, you will need to provide a written account documenting the loss of your passport and visa. Include a copy of the police report.

Is it possible to replace my lost US visa in new passport in USA?

NO, unfortunately you will not be able to replace a new US visa in USA. You will have to go back to your home country and get it replace with a new visa sticker there.

Source: US Visas- US Department Of State

Applying for a Replacement U.S. Visa

"Lost or stolen U.S. visas cannot be replaced in the United States. For replacement of a visa, you must apply in person at a U.S. Embassy or Consulate abroad. When applying for the replacement of a visa, you will need to provide a written account documenting the loss of your passport and visa. Include a copy of the police report."

Be ready to present the following documents in your home country:

• Your name, date and place of birth, and nationality.

• Your address and phone number.

• A photocopy of the lost visa, if available, or the date and place of issuance, if known.

• A photocopy of the bio-data page of your lost passport, if available. If not, the nationality and number of your lost passport as well as the issuance and expiration dates, if available.

• Circumstances of the loss: When and how your passport was lost or
  stolen.

• Copy of the police report for the lost passport

A US "visa" is solely for entering the US. The visa has absolutely no relevance to your stay in the US after entry. Since you are already in the US, you don't need to "enter" (at least not until you first leave the US), and thus you don't need a US visa. That is why it is impossible to get a US visa in the US (except for certain diplomatic visas), because, again, if you are already in the US, you don't need to enter.

After you leave the US, if you want to come back to the US the next time, before you come you will need to apply for a new US visa at a US consulate in the country you will be in at that time.