Il faut que I have only always seen with the subjunctive. But, of course, you can have il faudrait que (still followed by the subjunctive), where the verb falloir is in the conditional.
Similar with il vaut mieux que also requires the subjunctive.
About the last phrase I am not exactly sure what you mean. Were you thinking of something like:
Je pourrais faire mieux si je n'étais pas fatigué. -- I could do better if I wasn't tired.
That is a conditional clause and a different grammatical topic than the previous two. If you had something else in mind, can you clarify your question?