Smoke coming from the battery? Battery should still be under warranty, take it there to get it tested. the Focus has some weird wiring tied into the rear defroster. I cant recall right now what all else is tied to that fuse bank. But check the fuses and relays. Both under the hood and those in the cabin. the push on the gas and the radio may be just from poor grounding perhaps? feedback/noise from the motor is coupling on to the ground or to the antenna.
How long have you had the car? has anything changed since this happened?
2001 ZX3 Zetec - Rebuild "The TICK" (
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2004 ZX5 SVT - Restoration "Code Name Rocket" (http://www.focusfanatics.com/forum/showthread.php?t=722698&referrerid=62897)