Hi Deepak, Dubai is an interesting travel destination and won't be crowded during above mentioned dates. Coming to your question, you can easily get a new cellular connection (SIM) in Dubai. You just need to carry your valid passport proof copy with visa page for identification. You can buy the SIM card at the airport arrival area shops or telecom retailers in city. The price may be bit more. Other options are small grocery shops in Satwa, Bur Dubai, Karama and Deira. Checkout hotels/homestays in Dubai here as per your budget and interest: https://www.tripoto.com/hotels.
Home stay is quite not easy but you can book apartments at Damac and many more options you will get online they are not very expensive and you will feel like home