A tinyint column can hold values from 0 to 255 (if it is defined as unsigned) or -128 to +127 (if it is signed). The (1) in tinyint(1) is only for some formatting options and generally ignored. You could create it as tinyint(100) and it wouldn't make a difference.
Regarding the TRUE or FALSE, any int (int, tinyint, smallint, bigint) value can be used as (or converted to) a boolean value. It is considered FALSE if it is 0 and TRUE otherwise. So, 2 would count as TRUE.