Depending on the layout of the lights in the dash, you may be seeing bleed-over light.

For the brake light, check your brake fluid level first and if all is fine there, check to see that the brake safety level switch [attached to the resevoir cap] is working correctly, if so, check the emergency brake switch.

For the battery light, the only thing that will cause that to come on is when the battery fails to charge, whether it's caused by a dead battery, bad alternator, loose connection, or a weak short in the charging circuit. You may also want to check all of your under-dash fuses while you're at it.