The class depends on the type of fare paid. Usually Economy is referred as Y (usually Y is the most expensive ticket in economy as it has no restriction or so whatever) while F usually stands for First Class. Airline use this price discrimination schemes to extract the most amount of money from passenger who have different price sensitivity.
You can choose your seat online at their website
www.thy.com and use their online check-in feature.
quoted from the turkish airline site.
Online check-in is a service that gives a possibility to check-in online to all passengers who have a ticketed reservation before arriving to the airport.
The service provides check-in facility to the passengers from 24 hours up to 90 minutes prior to the departure time of their flights, through the web.
Also the passengers,
can select their seats by displaying the seat map,
can check-in online for the travel companies who are on the same reservation record (maximum 8 passengers at once), through check-in to the final destination or return check-in if they have return flights from the destinations on the same day.
Passengers with Electronic tickets,
who have completed their check-in procedures via our web site for Online Boarding Pass eligible stations are able to print their boarding passes.
for the later part i doubt that yo can print your boarding pass at home as i read that this feature is not available in dublin.