Questions

Given Equation is 

Mg + O2 → MgO

Balancing the Chemical Equation is nothing but Conservation of Matter. As Matter is Neither created nor Destroyed, it must be conserved.

Here we have 1 Mg and 2 O on the left side and 1 Mg and 1 O on the right side

To balance that, add 1 Mg on the left side so that it becomes 2 Mg and 2 O on the left side

i.e,

2 Mg + O2 → 2 MgO

Here it has 2 Mg & 2 O on the left side and 2 Mg and 2 O on the right side and the Chemical equation is Balanced.

In the given sentence,

Despite is the preposition. It does not take 'of' after it. Therefore, the grammar mistake in the given sentence is 'of'.

Hence, the correct sentence is  "She went to gym despite her illness."

Nebulous means hazy, Tiny means small, Vague means unclear, Insignificant means unimportant, Inadequate means in sufficient. So, Nebulous is nearest in meaning to Vague.