Multiplexer for low-voltage measurements
If your sources are thermocouples, then you don't have megohms source resistance, you have ohms, single figures of ohms.

The leakage current from HC4052 (which is a relatively high leakage part, you can find better speced ones) will be insignificant into your thermocouple source, even with respect to microvolts. While your meter may have megohms input resistance, the leakage current is sunk and controlled by your thermocouples.

Crosstalk is only an issue when you are dealing with AC, it's a capacitive coupling between the channels.

The timings you want are called turn on and turn off times, or delays. As a hint, when I search a long data sheet for something which should have particular units, for instance time, I initially scan down the right hand side of the table at the units column, to quickly narrow the search to relevant measurements.