Dual band antenna

Had few fundamental doubts on dual band antenna.

1. Is it possible to transmit two different frequencies with certain bandwidths (say, 2.4GHz and 5GHz) with a single antenna, SIMULTANEOUSLY ?
2. If yes, will there be multiple seperate sub-structures for 2.4GHz and 5GHz inside the same antenna?
(Because I have seen one antenna which has various structures combined together with a common feed source, thereby acting as multi-band antenna. I have also seen one, which has single dipole antenna which is designed for an operating frequency which is somewhere in between, say 2.4GHz and 5GHz, and then making it thick sized to increase the bandwidth on both the sides to meet 2.4 and 5GHz.)

Is it possible to transmit two different frequencies with certain bandwidths (say, 2.4GHz and 5GHz) with a single antenna, SIMULTANEOUSLY ?

Yes. Your smartphone typically has a combined 0.9/1.8/2.3/2.6 GHz LTE (for Europe) + 2.4 GHz Wifi/Bluetooth antenna system, and you can use WiFi simultaneously to LTE, so yes.

If yes, will there be multiple seperate sub-structures for 2.4GHz and 5GHz inside the same antenna?

That's not a meaningful question. What's a "substructure", anyway? These antennas wouldn't work as separate 2.4 GHz and 5 GHz antennas (if they did, the direct combination would lead to an impedance mismatch). If they do, there'd be an impedance matching threeport of some sorts, and then you wouldn't call it "one antenna".

have also seen one, which has single dipole antenna which is designed for an operating frequency which is somewhere in between, say 2.4GHz and 5GHz, and then making it thick sized to increase the bandwidth on both the sides to meet 2.4 and 5GHz

Yeah, but increasing the rod thickness of a dipole only increases the bandwidth of an antenna in a relatively small range around it's center frequency; it can't span multiples of the center frequency.