2.8V UART to 5V MCU - how?
For the 2.8V to 5V, since 2.8V is below most 5V system's \$V_{IH}\$, which is most often \$0.6V_{CC}\$, or 3V, you will need a buffer of some form.

The simplest method is to use any logic gate from the 74HCT family (they have TTL input thresholds) which results in a non-inverted signal.  Either a specific non-inverting buffer, or any gate whose inputs can be arranged to mirror their value to the output, such as an AND gate (74HCT08) with both inputs tied together.

For the 5V -> 2.8V a simple voltage divider would do the trick.

As for testing, the best command to send would be "ATI" and pressing return should result in information about the module being returned.

The full AT command set can be seen here: http://download.maritex.com.pl/pdfs/wi/MG2639AT.pdf