Peter, daylily rust doesn't overwinter on Patrinia, it overwinters as teliospores, the black winter spores, (not the orange summer spores except in very mild winter climates) on dead daylily leaves and then transfers to Patrinia in spring. Of course an existing infection can also overwinter as mycelium (fungal threads) inside any daylily leaves that can stay green and alive.
The spores are are just the reproductive units, like a plant seed, the actual fungal body itself lives inside the leaves feeding on nutrients from the plant's internal cells.
Heritage as a soil drench was found to control daylily rust for 120 days with a single application, a result that was comparable to 14-day interval foliar sprays, see Dong et al, 2013 : http://apsjournals.apsnet.org/...
Maurice, yes to 1 although technically it is not the teliospores themselves that affect Patrinia but their next spore stage but it amounts to the same thing.
For 2, daylily rust urediospores (the orange ones) can be deep frozen for use in lab tests at temperatures far colder than would occur in nature. So it is not cold alone that kills them outdoors but some combination possibly combining time, light intensity, moisture and temperature.
For 3 yes if the infected leaf dies, the mycelium inside it (the body of the fungus) dies too. In some rusts the mycelium can be killed by temperatures above that which would kill the leaves but nobody has tested this for daylily rust. So to be safe we assume that the leaves need to actually be killed to kill the rust. It is possible that the fungus could be killed a little before the temperature goes low enough to kill the leaf.