I need help understanding these 2 lines of code. Also why we used dot notation and not brackets?

As for using dot notation instead of brackets, both are fine. You can use brackets if you understand those better. Many JS developers seem to prefer dot notation so they use it more often (easier to type I guess), but both would work here: questions[i]["question"].

Looking at it piece by piece:

for (var i = 0; i < questions.length; i += 1) {
}

This is a for loop that iterates through an array named "questions." It will repeat the code inside it as many times as there are items in the questions array (that's what length is doing). Basic info about for loops here.

question = questions[i].question;

i is the numeric index of the for loop, so for the first loop it's 0, for the next it's 1, etc. questions[i] is just picking a specific item in the questions array, so for the first loop it's questions[0], which is the first item in the array since array indexes start at 0. questions[i].question is getting the value assigned to the question key in that specific array item. So if it was:

var questions = [
  { question: "Knock knock", answer: "Who's there?" }
];

then questions[0].question would return "Knock knock". Then that value is assigned to the question variable by using equals: question = (whatever).

The exact same thing is done for that array item's answer on the next line.