excellent, but let's say that for the NB transponder antennas greater than 100 cm are excessive. We say it for any new users who maybe worry, they think a big effort is required. For the NB transponder, a 40 cm antenna is sufficient for good activity. I repeat it only for new users.
Yes. If you can see the transponder noise floor there is little to be gained on receive with a larger antenna and even if you can't by as much as 10 dB you should still be able to copy easily signals at the same level as the beacon. That means a signal level about 19dB down on those reported by DD4YR above, i.e. a 20cm dish, should still be viable. I would not recommend that small but a re-purposed 45cm satellite TV dish should be sufficient.
On transmit things are different. Smaller dishes need more power. To reach beacon level I need 200mW-300mW or so to my 2.4m dish. This would imply needing 10W to a 45cm dish, but that level of power is readily available, so it's not a problem.
The reason I am using a larger dish if for digital television, which needs more power, but even then, 1.2m would be sufficient. The benefit of the larger dish here is the 6 dB reduction in power needed, around 5-10W instead of 20-40W. For DATV you need a very linear amplifier and that's more difficult, but not that difficult.
In other words don't be put off by only having a small dish!