1. It generally should not be a problem,. Eastern part of Slovakia tends to be a bit racist, but it rarely goes beyond stares.
To reach Bratislava, take cogwheel train to Strba and change for train towards Bratislava. Alternative option is to travel via Poprad (this allows you to take more comfortable IC trains). Use http://www.cp.sk to find ideal journey for you date and time.
Thanks a ton! This helps