How frequently do trains run between the two stations? Are the trains full, or can I just show up at the railway station and get a ticket?
There are trains between these stations once in every two to three hours.You can show up at the railway station and get a ticket. Buses are more frequent and I would suggest that since the journey is not long.
In kerala, for short journeys you can always show up at the station and take a sleeper ticket for your destination and enter any sleeper coach. In your case aleppey to ernakulam has lot of trains between them just check up at the counter for the next train while taking a ticket and you are good to go.
there are lot of trains in eranakulam to alappey . And u don't want to reserved in short journeys, u can get sleeper class ticket in counter and u can travel the sleeper class and also available chair cars and passenger trains ... this the link for train availability to alappey