In general, if you need a 7.5v supply the most obvious answer is that you would use a two cell battery pack. The operation range would be 8.4v-5v from full to flat, the useful range would be from 8.4-7 or so for most applications.

Boost converters are generally not necessary in this hobby since LEDs operate at less than battery voltage. Some saber boards do incorporate boost circuits either because a chip (usually the speaker amp) requires higher voltage. These are usually only for milliamp loads though.

Depending on how much you want to boost, you will need some excess of amps from the battery. If you want to boost from 3.7 to 7.5 at 3amps (according to a few calculators I checked) you might need as much as 10-15A out of the battery.

Going in the other direction, a buck converter will still waste some of the energy as heat, but since you are starting from a higher potential, the demands aren't as severe. If you have a constant current driver, the intensity will remain even until there isn't enough current to drive them. Some boards do incorporate these to drive the LED.

As for resistors, the intensity of the LEDs will change over the discharge curve of the battery. A full battery is 4.2v and the minimum safe discharge is 2.5v. The protection circuit should prevent it from going lower. They are also cheaper and easier to calculate and install.

It's really more complicated than all of this, but if you want to learn more than I recommend doing research on electrical engineering forums.