Merging Questions In Irish
In American English, we can ask for several bits of information in one question. For instance, suppose you want to know the following bits of information:

1. When did you take these photos of yourself?
2. Where did you take these photos of yourself?
3. Why did you take these photos of yourself?

All three of these can be merged into one question like this:

"When, where, and why did you take these photos of yourself?"

This saves the person who is asking the question some time and breath since they don't have to repeat "did you take these photos of yourself" which appears in all three questions several times. Can the same be done in Irish?

Also, various interrogative words like "when", "where", etc. take the direct relative after them and some take the indirect relative, so if you can actually do this in Irish, how do you determine which relative to use? Do you just use the relative associated with the last interrogative word appearing in the question?

Question

Merging Questions In Irish
In American English, we can ask for several bits of information in one question. For instance, suppose you want to know the following bits of information:

1. When did you take these photos of yourself?
2. Where did you take these photos of yourself?
3. Why did you take these photos of yourself?

All three of these can be merged into one question like this:

"When, where, and why did you take these photos of yourself?"

This saves the person who is asking the question some time and breath since they don't have to repeat "did you take these photos of yourself" which appears in all three questions several times. Can the same be done in Irish?

Also, various interrogative words like "when", "where", etc. take the direct relative after them and some take the indirect relative, so if you can actually do this in Irish, how do you determine which relative to use? Do you just use the relative associated with the last interrogative word appearing in the question?

Answer

You can merge questions in Irish as well:
Cén uair agus cén áit agus cén fáth ar thóg tú na grianghraif seo díot féin?

As for the direct and indirect relative, you could probably get away with doing as you said and using the kind of relative associated with the last question word:
Cén áit agus cad é mar a thóg tú na grianghraif seo?
Where and how did you take these photos?
But from the point of view of style, I think it would be more natural (níos gaelaí) to say something like:
Cén áit ar thóg tú na grianghraif seo agus cad é mar a thóg tú iad.
Repeating yourself doesn't sound as superfluous in Irish as it does in English.