If most of the daughter element dissipates, won't samples date much older than they should?
No, in the rarely-used-today simplistic methods such as K-Ar, they will date much younger than they really are. In the more sophisticated methods either no date will be produced or the correct date will be produced.
And isn't it impossible to determine that hasn't happened?
No, the most widely used methods such as Ar-Ar and U-Pb detect that occurrence and often produce a valid date anyway.
And even if that problem were solved, if decay rates were greater in the past, won't samples again date much older than they should? And isn't it impossible to know past decay rates?
It is not impossible to know past decay rates. Radiometric decay depends on the most fundamental properties of the Universe, and any significant change at any time after the first microsecond or so after the big bang would be detectable in other measurements.
If decay were accelerated enough to fit a YEC time frame there would be subtle traces left. There would be no water left, the surface of the Earth would be molten, and there would be no life other than possible some thermophilic bacteria.
U-Pb and Ar-Ar include an internal check on the premise of no significant material lost or gained by taking multiple measurements on one sample. Ar-Ar heats the sample to progressively higher temperature until it's vaporized, measuring the argon released at each step. U-Pb measures the isotopic ratios at different places even on a weentsy sample (measurement volume as low as 10μm diameter and 1μm deep). Different "dates" from these individual measurements indicate the system has not been closed or there was extra daughter isotope at solidification.
Even when the system is not closed or, U-Pb and Ar-Ar often produce a valid date. E.g. in the tour-de-force dating of the eruption of Vesuvius in 79 AD by Ar-Ar at the Berkeley Geochronological Laboratory they detected the presence of "excess argon"; argon that was trapped at solidification. They got the correct date. Plain K-Ar would have produced a date that was too old.
You did miss one of the YEC triad. The amount of daughter isotope at solidification must be known.
For K-Ar and Ar-Ar, argon easily escapes from lava as the pressure reduces at the eruption, so mostly no daughter isotope is present at solidification. Cases in which this is not true are well known, and Ar-Ar can detect this trapped "excess argon" and often produces a valid date anyway.
U-Pb, mostly performed on zircons, takes advantage of the fact that uranium and thorium can easily substitute for zirconium in the crystal, sometimes as high as one weight percent. But lead doesn't fit big time, either physically or chemically. So the initial daughter isotope amount is zero. Even the RATE group (comprised of the only YECs who understand the process) acknowledges that the only significant source of lead in zircons is radioactive decay.
Isochron methods (not used for dating much any more) produce the amount of daughter isotope at solidification as one of the results of the method.