I have a 5V/1.5 A power supply lying around. Will this be sufficient for the pi b+ model?
Normally, the specification for the power supply is 5V DC and 700 mA.
In addition, if the external USB peripherals or WiFi Dongle are used along with the Pi, then there is requirement of power supply with specification 5V and 1.5A or 2A.
It should be noted that don't use cheap power supplies, which may not capable of providing reliable 5V.
One can also use smartphone chargers (terminated in the micro USB plug), which mostly possess same specifications i.e. 5V and 700mA. But, check it out before starting the project.
Maybe - it depends.
If it's a modern switching type supply it should be fine. If it's some old thing you have lying around it might be "nominally" 5V and have poor regulation and maybe as much as 7 or 8 volts when lightly loaded.
I can't tell which you have from here