Electronic – Continuous-conversion vs Single-Conversion mode

The typical way to do this with a single micro is to establish buffers in and stuff them up with ISRs (interrupt service routines) triggered by the reception of serial GPS data or I2C data. Set a flag when an entire message is available in the buffer and read it with your background routine. At 4800 baud you've got a leisurely 2000 microseconds or so between characters so even if the hardware buffer is a single character you have lots of time to do other things. If you double buffer you only have to worry about the inter-message time rather than the inter-character time.

The AVRs have decent interrupt handling and you can probably write everything in C if you want.

There is some confusion here since you state that the gyroscope is giving you readings where the software indicates that it is the gyroscope that wasn't initialized.

The accelerometer is integrated into the same chip as the magnetometer which on that breakout board is a STM LSM303D(datasheet ). This chips contains a MEMS type magnetic field sensor. STM is secrative about the exact type of sensing element, it is likely that it can be succeptible to damage at strong magnetic fields and the high flux density and divergent field lines close to the surface of a magnet may cause other damage.

The surface or rare-earth magnets (e.g. neodymium) can have considerable field strength near the surface, if you bring the magnet very close to the sensor the field strength can be a significant fraction of 1T and there may be enough flux density to significantly damage a sensitive device like a mems sensor.\$1000\mu\ T\ = 10 G\$ which the magnetometer datasheet says should be fine, but I suspect the strength of the field was a good deal higher. The constant readings and software error message is likely indicative of damage to the relevant sensor chip the readings being garbage data or default values from an uninitialized sensor.

In general there are any number of ways that a strong magnet close to the board can cause damage to one of the sensor chips. A uniform 1milliTesla field is probably less damaging than the highly divergent field at the business end of a magnet.

The magentometer/accelerometer should handle magnetic fields up to 10,000 G according to the datasheet, however I suspect that the gyroscope (the device giving you an error message) with its mems gyroscopic sensor (likely a PZT but STM doesn't say) may be more susceptible to damage (datasheet).