Do two 1.5 batteries wired together produce three volts--or just 1.5?

Answer 1

Two batteries in series = 3V.

--[- +]---[- +]---3V
|_____________0V

If batteries are in parallel, you get 1.5V, but you double the amp-hour capacity of the arrangement, so 1.5 V will be produced for a longer time.
In series, each battery has say, a 1/2 amp hour. That means the series set up will produce at least 1/2 an amp at 3 volts for one hour. The parallel setup will produce only 1.5 V at 1/2 an amp for 2 hours.