'Would' is being used to make a suggestion. It really has nothing much to do with conditionals. It has more to do with habit, if you like, but as you say it is a polite and rather non commital or tentative way of making a suggestion for your own actions, in this case. A is correct.

Do you suggest or would you suggest?

'Would' is being used to make a suggestion. It really has nothing much to do with conditionals. It has more to do with habit, if you like, but as you say it is a polite and rather non commital or tentative way of making a suggestion for your own actions, in this case. A is correct.

What does I would suggest mean?

I would suggest' is more indirect and suggests that you have an option and it's up to you choose.