That will depend on things like where you are from, where in the world you are going to meet your Irish boyfriend and how long you plan to be with him.
Yes
yep
Slovakia is in EU and therefore you don't need tourist visa if you are Irish cityzen.
Yes sure
Yup
Yes you do, even for tourism visits. There is a Thai Consul in Malta at Bisazza Street, Sliema.
If your boyfriend comes back with a Visa, you are able to marry him in the United States. You will need to get an immigration Visa rather than a tourist Visa.
yes
Yes
No. Bulgaria and Ireland are both part of EU.
No. Both Ireland and Cyprus are members of the European Union and there are no visa requirements for EU nationals.
Ireland is not part of the Schengen Area so Schengen visas are not valid in Ireland (or the UK). You may need a visa unless you hold a passport from a country which doesn't need a visa for Ireland (e.g. USA). Check the Irish embassy for your country to see their rules.