You stated that in the future there will be some steps with a multiple choice option. In this case you will need the «continue» button anyway.
But there is another reason to use the continue button. An interaction should always only trigger an expected action. In this case the user might not expect to trigger a continue action when selecting the answer. If a user is not quite sure about about an answer she would have to go a step back.
But I see other issues as well. your implementation of the «back to last question» on the second question would rather communicat to go back in a hierarchy like a level up in a menu or something like this. If the user should have the possibility to go back to the last question (which is just a series of questions on the same hierarchy level) you probably should use a back button left of the continue button.
If you have some questions with single choice and some with multiple choice, make sure this is communicated to the user. A well known pattern is radio buttons vs. checkboxes. I'm not saying you have tu use these but make it clear to the user.
An another point. Maybe you should consider to give the user a hint of how many questions in the questionnaire will be. I do not mean be an exact number but maybe with some kind of progress indicator.