Can I claim my niece and nephew ?

What about their Father?

Their father is not around and will not be claiming them on his tax return.

Yes, you can claim a relative on your return if you meet the requirements for claiming a qualified relative. Please see the information below to determine you if you meet the requirements. 

Qualifying Relative Requirements

https://ttlc.intuit.com/replies/3288503

Qualifying Child Requirements

https://ttlc.intuit.com/replies/4835245

Please see the IRS publication on Personal Exceptions and Dependents for more information. 

If a child has resided in your home for more than 6 months out of the year and you provided all necessary support, then yes you can claim them as dependents when filing your taxes. You need to make sure that no one else can claim them as dependents first or that there is not a contract in effect regarding taxes between the birth parents (like divorce decree or waiver releasing the ability to file to only one parent).

Yes you can. When you enter dependants check other and specify what their relation is to you. Irs might want to see proof but usually they just send it through.