"In an Irish set are all the three tunes in the same key?"

Usually, but not always. Often one will go from the major to the relative minor - such as G major to E minor.

Then there are modal keys. D dorian is the most usual - start with D on the piano and play only the white keys. It sounds like a minor scale, but not quite - the 7th note of the scale is flatted. Some modal tunes can be played with just one chord as a sort of drone - for example Dm for a D dorian mode, or perhaps with with a Cmajor thrown in when needed for harmonic reasons.

And another comment: when tempted to accompany a singer, listen carefully first. At times when I sing or play a slow air with a free meter, accompanyment is not wanted, in fact it can throw the whole tune or song off. Knowing when not to play is just as important as knowing when and how to play accompanyment.

S. in Seattle