HRA and Housing Loan

In your case when rental income offered to tax, HRA claim will be allowed.

1. Though both sec 24(b) and 10(13A) are different and operate independently. The practical scenario in most of the cases is that they would be having a house property and repaying the loan on the same and stay in another house and claim HRA exemption u/s 10(13A) 
2. The important point is both the above section operates exclusively and one is in no way operates with other. Hence, if an assesse as long as he satisfies the conditions for claiming HRA u/s 10(13A) ( by staying in a rented house other than his own house ) he can avail the benefit. 
3. With respect to housing loan repayment ( principal and interest ), the same can be availed as long as the conditions attached to it is fullied. If the rent received on house is shown under Income from house property, interest paid on the same can be availed and the same will be considered as cost while computing capital gains.  
4. So both sections operate separately and the assessee can be benefitted. 
Yes. both can be very much claimed. 

1. As long as you satisfy the conditions attached to sec 10(13A) and sec 24(b), both can be claimed. 
2. In your case since you are staying in a rented house and paying rent, HRA exemption u/s 10(13A) can be claimed. 
3. However with respect to interest on housing loan u/s 24(b) it can be claimed only from the year in which the construction was completed. Pre-construction interest in 5 equal installments can be claimed once the construction was completed. Interest to the extent of Rs. 2 lakhs will be allowed as interest on borrowed capital. 
Please correct me if the above solution has an alternative view.