As to the commonality of the C/C# it is the least used of the half step "Irish" boxes..
In order of popularity B/C, C#/D, D/D#, C/C#
As Andy mentioned the C/C# is usually used as a 1/2 tone higher box playing the B/C style..
I have met only one player of C/C# in the States and he usues it rarely, usually plays B/C

However C/C# was very well known in Scotland and England before WWII And early on the Wyper Brothers
were known for the C/C#

Those early players played for the outside in as if it were a piano..

The Irish players play from the inside out..rarely playing in the key of C but in D the common Irish key as well as G and relative minors...

Klezmer.. I don't think so.

As to the style... very much looks like an early 1900's 2 row with open pallets...

I think Eric Martin's three row is even more interesting.......

As for that one row.. I'd even consider retuning it C#/D much more useful

Very informative indeed. I was thinking such a box would be most useful played outside/in as you describe. Basically a chromatic box (like a piano). Might be a useful substitute for a regular piano accordion.
Irish is a world unto intself. I tried a B/C box for a bit and found it rather interesting, but gave it up. I also play penny whistle and low whistle and I find that instrument suits me much better for Irish tunes. I have thought about getting a D/G box someday. Change it to a D/G and have it "Cajun" tuned, Eric's two row might be great fun.

If you "Cajun " (just) tune a 2 row you may have some ear wracking experiences playing cross row...

Better to tune Tempered and dry far more flexible
for a wider variety of styles

If you want to hear "Irish" trad on a dry tuned 3 reed
2 row give a listen to Tim Eady's first CD entitled
"Tim Eady"
you can also find him on youtube

A great fan of Eric MArtins 2 rows and a great French diatonic player and CAJUN style player is Yann Dour

More details about tuning I didn't know. I guess Cajun boxes are one row for good reasons.

John, thanks for the word about Tim Edey! Man, what a fantastic player. I've never heard any Irish accordion player use such beautiful combinations of chords. Awesome stuff

People check that Tim Edey dude out!

http://youtube.com/watch?v=pj8Gk6V-Rec&feature=related

You're welcome

Just for clarification

Tim Eady is English

The tune is not "Irish"

And I believe he is playing a Saltarelle Nuage in a 5th (4th) apart system.. my guess D/G..

An "Irish" tuned box would be B/C,C/C#,C#/D,D/D#

He mentioned he was going to play with Brendan Power.. a phenomenal harmonica player from New Zealand I believe...

I also understand that Eady may be messing about with
B/C box but due to the fingering and the chords I think it was a D/G
His self titled C/D was in D/G

Note that also on youtube you can see him play "melodeon" the one row accordeon..

excellent player in may styles...

Also plays guitar and piano