Can’t replicate this – I downloaded your file, and it behaves as I’d expect here: if I copy-paste a frame or alt-drag to make a copy of the frame, the applied character styles remain the same in the copy as in the original.
CS6 Mac 10.6.8

Sounds like you might need a version control system like they use for software development. CVS, SVN, Git etc etc. Check files out and in to a system. I think there are open source free ones.
Takes a bit of persuasion to get some people to use them, but worth it in the end.

I’ve regularly dealt with tables of up to and over the 10,000-row limit, with a single table running to over 100 pages in InDesign, with only very rare crashes (and those not obviously related to the table structure). Predominantly CS3 and CS4 though (yes, another client who sticks with what works rather than upgrade pointlessly).
The content arrives as tagged text (para styles already set), and is converted to a table in InDesign, with table and cell styles then applied afterwards. Also many cells are manually merged afterwards. If there are more than 10,000 rows in the imported text, it still makes a table successfully, but you can’t then add (insert) any more rows.
Applying a style or a cell attribute to a whole column of a very large table can take many minutes, but it does it reliably.
The only difference I can see from the case above is that these are all in single-column frames.
As for Word and large documents/tables, I’ve had way more crashing problems there.
Chris.

Would a table work? One language per table column, one row per paragraph (so long as the paragraph numbers match), invisible table cell divider lines.

Be aware that English usually runs shorter than most other languages for the same content, perhaps by 20-25%.

Good luck,
Chris.

You can get all the text in a story to disappear by applying “No Break” to all of it. Then it effectively becomes all one long line that can't possibly fit any text box.

Why would you want to do that? Well I'm glad you asked me that. It was a document using an old font which “re-used” all the code points for various characters in one of the Indian scripts, such that the text was only usable with that particular font – any other font and it showed rubbish text – and you had to change font every time an English word like a company name was used.
Some of the re-used code points would be punctuation marks in any sane font, so InDesign would break lines in the middle of words. Fixed by applying No Break to everything and then taking it off spaces and anything else where you wanted a break to be allowed.

Someone's got to say it: be careful about doing this globally, as there could be occasions when you want a single letter word to remain on the first line.

Arguably in your example, “piggy and I” belong together as the subject of the verb, and the text would read better that way.

For another example, “King Henry V” might be better not to be split over two lines (could be achieved with a non-breaking space).

Other languages might yield some exceptions. Russian and Polish certainly have single-letter prepositions, which obviously work better at the start of a line than at the end. In Italian, a, e, i, o, è are all single letter words (to, and, the, or, is). Tried to find a resource with general multi-lingual guidance, but no such luck.

And just to confuse things further, Hart's Rules for Compositors and Readers (Oxford University Press, 1967) has plenty of instances of single letter words at the ends of lines, and has no “rules” to cover this eventuality.

Does master page with a text box the right size meet your requirements?

I can see from the invisible items in the pictures that the individual lines of items 6, 7 and 8 use pararaphs to separate the lines. Items 3, 4, 5 only have one paragraph mark per item, while 6, 7, 8 have three per item. Does the column splitter rely on paragraph marks to work? What happens if you use “new line” instead of “paragraph”?

Another thought, would text to table help in this context, where you can specify row and column break points?

PS I don't have CS5 to try it out.

PPS Just tried with new line instead of para for new lines within an item, and paragraph between items.

Then using text to table, row separator=paragraph, column separator=paragraph, total columns=3 you get a table of 3 columns, split where you want it, with the “vertical” items 6, 7, 8 remaining vertical.