Can the gate-source voltage be negative?

Question

Electronics

In the datasheets on the mosfet, I see that the following characteristics are constantly indicated:

Answer 1

Maybe for p-channel transistors it is usually written with a minus. This is fine.
In the case of the upper switch, the gate is connected to the source through a resistor and on it the potential is equal to the power supply. To open the key, we pull the gate to the ground potential and thus the voltage at the gate is less than at the source, i.e. negative.
In general, as a rule, a gate-source voltage can be applied in both directions, for example, up to ± 20 V.

Answer 2

Either the transistor has a so-called. "Built-in" n-type channel (more typical for field-effect transistors with a control pn-junction). So without specifying the source of the table - the question is not complete.
Judging by the intended level conversion scheme for I²C, you are trying to select the wrong transistor.