No, you should not bring notes. Some interviewers may deem it unprofessional. Even among those that don't, it may put you in a poor light compared to other candidates. It is not worth the risk.
I've been on the interview panel for a number of software development jobs, and I've never seen a candidate bring notes. If someone did, I cannot say for certain that I would not react to this negatively.
Consider: you state you want notes to cover the questions you're planning to ask the interview team and prepared answers to possible questions. If I'm going to an interview, I try and prepare four or five questions. I would expect most candidates to be able to commit that many to memory ahead of time.
In the second instance it could cut both ways. Some people might think it demonstrated thorough preparation and dedication, which is a good thing. On the other hand, if you refer to notes in answer to personal questions such as "tell me about a time you worked as part of a team", it could be taken as a sign you are not giving an honest answer.
Other answers have said that they might find it understandable behaviour from a graduate or someone who was clearly nervous. However, a good interviewer ought to be able to make allowances for that in their judgement. If you take notes, you are effectively assuming the interviewer will treat them with good grace. It it likely to be less risky to assume the interviewer will compensate for your nervousness in other ways.
If you do refer to notes, I would warn the interviewer at the beginning that you wish to do so and state your reason. You could also offer to show the interviewer the notes to demonstrate they are nothing but simple reminders to steady your nerves.
In short: interviewing is, sadly, a pathetically inexact science and different interviewers will do and expect wildly different things for similar jobs. But I would err on caution and not refer to notes.
There may be a cultural issue here. I'm in the UK, and I'm presuming the OP and other respondents are in the US.