Yes, a Schengen visa holder is allowed to go to all the countries that are a part of the Schengen region, see and explore them!
Yes, a good travel insurance that provides a minimum coverage of €30,000 and it should cover the medical emergencies.
You can book a Schengen visa appointment in the Dublin any time you want but it must be at least 15 days before your planned dates of visiting the Schengen countries.
You can fill the online application form to book your appointment online. However, on the day of the appointment, you will need to attend the visa centre with your paperwork for documentation and biometrics.
The standard documents that you need to submit include the duly completed Schengen visa application, a valid passport, recent passport-size photographs, proof of travel, proof of accommodation, proof of finances, cover letter (if necessary) and travel insurance.
The standard processing time for the Schengen visa is anywhere between 10 to 15 days. Within this duration, you will be able to obtain your Schengen visa. However, it may take longer during special circumstances like peak tourist times or if additional documents are required.