Can I make and receive phone calls using a tablet with a SIM card slot in it? I have an Android tablet without telephony capabilities. I can put in a SIM card. When somebody calls my SIM card number (mobile number), can I receive this call? What application do I need?
No, you usually can't receive calls with an tablet which doesn't provide this functionality. The SIM card slot is only for mobile data communication and there is no way that you just download an App which enables GSM phone functionality (AFAIK).

You can use VoIP though.