Generally speaking, this is not a valid format in English. All of the examples you gave there have a verb that can be considered conditional. With those verbs, you can turn something into a question just by reversing the subject-verb order, so that
It is red.
Is it red?
"I should bother", while grammatically correct, sounds very strange to a native speaker. But its question form, "Should I bother?", is perfectly valid. I don't know how to explain that one to you, but I would use "I should care", but "Should I bother?" and "Should I care?" are equally valid. If anyone knows why, I'd love to hear it too.
These phrases can also be modified with a question word to change their meaning, so "Can I fix this problem?" just asks if it is possible, while "How can I fix this problem?" asks for an explanation or procedure for fixing the problem.
As always with English, there are many nuances. One is that, unfortunately, I can not tell you what verbs the above construction works with. It's something that I just know from experience. "Is", "can", "should", "would" all work this way, but "fix" does not. Instead, you modify "fix" with one of the other verbs, in your example "can".
Last but not least, you can make what I'm going to call declarative questions. This is where you take a declarative statement, and do nothing but add a question mark, and now you are asking if the statement is true or false. Your "It is red?" is an example of this. It implies that you hope or expect the statement to be true, but desire confirmation. I'm not sure this is really grammatically correct. It probably has no place in formal writing, but it is a common construction in conversational English.