Sure you need 1 resistor per Led in parallel. But if wanting to run upto 7 or more LEDs off one battery you end up with the condundrum the OP ended up with needing a 22v battery. Resistors are cheaper than batteries especially big ones.
Absolutely, for the reasons stated. I didn't mind cooking LEDs when somebody else was paying for them, but it became a different story when my wallet was involved. LEDs are not resistors, they will take as much current as they can once their Vf is exceeded, right up to the time that they die. They do glow very brightly while doing so.
You can arrange 7 LEDs as two strings of three plus a resistor each, having ensured that all in each string want the same current, plus a solo with its own resistor, and they will probably run for days on a PP9. Longer if you have a way to switch them off.
Or, 3 of PP3 in series gives 27 volts. If the string of 7 plus resistor runs off that, assuming a capacity of 4.5AH (Duracell info) a current draw about 15mA should last about the shelf life of the batteries.
Sometmes the simple answer, if too simplified, can lead to problems.