The ability of Sorcerer's Broom is a triggered ability, not an activated ability. It doesn't allow you to sacrifice a permanent whenever you want; rather, you need some other way of sacrificing permanents, such as the activated ability of Food tokens.

If you sacrifice Sorcerer's Broom and another permanent at the same time, Sorcerer's Broom's ability triggers for that permanent.

While resolving the triggered ability of Sorcerer's Broom, you can't pay {3} multiple times to create more than one token. However, if you control more than one Sorcerer's Broom, you can pay {3} for each of their abilities.

The token will have Sorcerer's Broom's ability. It will also be able to create copies of itself.

The token won't copy counters, Auras, or Equipment on Sorcerer's Broom, nor will it copy other effects that have changed Sorcerer's Broom's power, toughness, types, color, and so on. Normally, this means the token will simply be a Sorcerer's Broom, but if any copy effects have affected that Sorcerer's Broom, they're taken into account.

If Sorcerer's Broom leaves the battlefield before its triggered ability resolves, the token will still enter the battlefield as a copy of Sorcerer's Broom, using Sorcerer's Broom's copiable values from when it was last on the battlefield.