Will the Uno be able to power the RFID, accelerometer, piezo and 3 LEDs or will I need to use a external power source?
Also, I want the 'food' and 'drink' LED's to notify the user about every 30 minutes. Will I be able to code this in or will I need a timing device of some sort?
Yes the ARD will be able to power all of those, as for notifying the user every 30 minutes, that you may want to use a clock circuit of some kind. Yes you can do the timer with the ARD but it will look something weird like this.
delay(1800000) => 30 minutes OR you can use a nested loop like this,
for(count = 0; count <= 30, count++) // 30 minute delay
for(count2 = 0; count2 < 60; count2++) // 1 minute delay
delay(1000); // 1 second delay
Hope this helps.