Your condition in your for-loop is wrong. You have an assignment instead of an evaluation.
for (i = 1; i=amount; i++)
You should be creating elements and appending them to the DOM. Avoid using document.write. Also, please begin indexing at zero, unless you need to start at 1.
Update
If you provide a name attribute to your input fields, they will be submitted with the form on submit.
input.setAttribute('name', 'answer[]');
When you hit submit, the input field values will be sent to the server as:
answer=foo&answer=bar
or:
{ "answer" : [ "foo", "bar" ] }
Refer to this if you are still confused: POST an array from an HTML form without javascript
Example
let amount = prompt("Please enter the amount of questions you would like", 5);
let questionForm = document.getElementById("question-form");
let answerList = questionForm.querySelector(".answer-list");
for (let i = 0; i < amount; i++) {
let inputWrapper = document.createElement('DIV');
let label = document.createElement('LABEL');
let input = document.createElement('INPUT');
input.setAttribute('type', 'text');
input.setAttribute('name', 'answer[]');
label.textContent = 'Answer ' + String.fromCharCode(i + 65) + ': ';
inputWrapper.classList.add('input-wrapper');
inputWrapper.appendChild(label);
inputWrapper.appendChild(input);
answerList.appendChild(inputWrapper);
}
.input-wrapper {
margin-bottom: 0.25em;
}
.input-wrapper label {
display: inline-block;
width: 5em;
font-weight: bold;
}
<form id="question-form" class="modal">
<div class="answer-list"></div>
<button type="submit">Submit</button>
</form>