Can one take valium (5-10mg/day max, only as needed) and (bayer) aspirin (regular dose, one pill 3-4 times a day) together for one week?

Yes, usually okay.: Very low to almost no potential for problems from taking Valium and aspirin as you described for one week, though 5 mg of Valium twice a day rather than 10 mg once a day may provide somewhat better control of anxiety. Suggest avoiding Valium and similar medications if you have a personal or family history of alcohol problems due to high potential for addiction.