Absolute maximum ratings vs recommended operating conditions: which datasheet values do I design to?

Absolute maximum ratings are damage limits, not operating limits. Beyond them the part may be permanently harmed; at or below them the manufacturer promises only survival, not correct operation, and usually adds a note that prolonged exposure near those limits affects reliability. They also apply one at a time, not all together.

The recommended operating conditions are the range in which the parameters in the electrical characteristics tables are guaranteed. So 3.9 V is outside the specification even though it is below 4.0 V: the chip may run, but nothing in the datasheet is promised any more. Design to the recommended range and keep your supply tolerance inside it; a 3.3 V regulator at ±3 percent gives 3.2 to 3.4 V, comfortably within 1.8 to 3.6 V.

Same reasoning for the pin current. The 25 mA figure says the pin will not be destroyed. The 8 mA figure is the test condition at which the output voltage is guaranteed, for example a high level of at least VDD minus 0.4 V. At 20 mA the pin voltage will be lower by an unspecified amount, so the LED current is not what you calculated. There is normally also a limit on the total current of all pins together and per supply pin, which a few heavily loaded pins can exceed.

For a 20 mA LED, use a transistor, or pick a high-efficiency LED that is bright enough at 2 to 5 mA.

On the columns: typical values describe an average part at 25 °C and nominal supply. They are not tested on every unit and are not guaranteed. Min and max are the guaranteed limits under the conditions stated in the table header and the conditions column, often across the full temperature range.

Use the worst-case limit that hurts your design. For an input threshold, take the maximum V_IL and minimum V_IH. For battery life, take maximum supply current. Use typical values only for estimates, and treat the graphs the same way, since nearly all of them are typical curves.

Always read the conditions next to a number. A MOSFET's on-resistance quoted at V_GS = 10 V tells you nothing about its behaviour at 3.3 V, and a regulator's dropout voltage quoted at 100 mA is not the dropout at 1 A.

Thermal limits are the ones most often missed, because a part can be inside every electrical rating and still overheat. Junction temperature is T_J = T_A + P × θ_JA. A linear regulator dropping 12 V to 5 V at 0.3 A dissipates 7 V × 0.3 A = 2.1 W. With a junction-to-ambient thermal resistance of 50 °C/W and no heatsink, that is a 105 °C rise, or 145 °C in a 40 °C enclosure, above a 125 °C junction limit even though 0.3 A is far below the 1 A current rating.