Which of the following equations represents the first law of thermodynamics under isobaric conditions?

Given below are two statements.
Statement-$I$ : Adiabatic work done is positive when work is done on the system and internal energy of the system increases.
Statement-$II$ : No work is done during free expansion of an ideal gas.
In the light of the above statements,choose the correct answer from the options given below.

Which of the following statements regarding the first law of thermodynamics is correct?

The $\Delta U^o$ of combustion of $CH_{4(g)}$ at a certain temperature is $-393 \ kJ/mol$. Then the value of $\Delta H^o$ is:

$A$ cup of water at $5^{\circ}C$ (system) is placed in a microwave oven and the oven is turned on for one minute, during which the water begins to boil. Which of the following options is true?

For the gas phase reaction $A_{2(g)} + B_{2(g)} \rightarrow 2AB_{(g)}$ taking place at constant pressure and temperature where all gases are behaving ideally,which of the following must be correct?