"Can you understand Irish?"
Translation:An féidir leat an Ghaeilge a thuiscint?
Nope, because Gaeilge isn't a plural. You can use an Ghaeilge, however, which is what's shown as the translation here.
What is the difference between an Ghaeilge and na Gaeilge, and as Gaeilge?
an Ghaeilge is the nominative, when speaking abouy the language in a broad sense. na Gaeilgej is genitive. as Gaeilge is when you speak as Gaelige*