Do 3G and phone calls(gsm) use the same antenna in a mobile phone?

Your connection to the cellular network, no matter the "G", always uses the same antenna. You can see this in a teardown of whatever phone you have. For instance, here is a teardown of my phone:

HTC Thunderbolt Teardown

In the last photo, you can see that the LTE and EVDO antenna is one and the same. This also handles your 2G connections as well even though they all operate on different frequencies:

Cellular Frequencies

What you are doing when you disable your data, is shutting off the modem in the chip that talks on a particular frequency. Each cell phone has several modems. For 2G, 3G, 4G, Bluetooth, etc. Since the "Gs" are similar in the way they operate, they can use the same antenna. Bluetooth and WiFi operate very differently and require different antennas as can be seen in the teardown.

2G connections provide voice and text and, since it's the oldest, has the widest coverage. 3G provides voice (GSM only, see below) and data on the same frequency, and, in some model phones, at the same time. 4G provides data only and voice is either done by falling back to a different communications model (frequency/"G") or via voice over IP. So when a 3G or 4G signal weakens in a particular area, there is usually a 2G signal to fall back onto but it will only provide voice and text.

There are some interesting notes in the Wikipedia article on 4G if you search for the word "voice". Such as:

EV-DO is not designed for voice, and requires a fallback to 1xRTT when a voice call is placed or received.

And:

Since the 2.5G GPRS system, cellular systems have provided dual infrastructures: packet switched nodes for data services, and circuit switched nodes for voice calls. In 4G systems, the circuit-switched infrastructure is abandoned and only a packet-switched network is provided, while 2.5G and 3G systems require both packet-switched and circuit-switched network nodes, i.e. two infrastructures in parallel. This means that in 4G, traditional voice calls are replaced by IP telephony.

Another thing to note, is that while voice requires less bandwidth, it requires a continuous connection. Whereas data can be packetized. A good discussion of how voice and data share the network (when both are available) is available in the following article on Using data versus voice in an emergency

No. The cellular voice and data go over the same channel and therefor use the same antenna. Often the up and down links are at different frequencies, so different antennas (or at least different performance characteristics) are used. But the division of labour has nothing to do with Data vs Voice.