There was a spelling reform in the 1950s. And a lot of words lost their silent letters, including first names and surnames. But some people still like to use the older spelling. So if you want to use Ó Corraidhín that's fine. It's probably the spelling your great-grandparents used, except that they'd have a dot on the D rather than then H.

Until the last century Irish was written with stylised fonts similar to the Book of Kells. But it was still the Roman alphabet though.

Ogham goes way back, as far as I know there aren't any manuscripts with it, it was just carved into stones, but I could be wrong about that.

I’m not an expert but apparently ogham was used to some extent during late middle ages in some manuscripts, and taught to poets for a fairly long time, see scholastic ogham on Wikipedia.

I don’t think we have any extensive texts in it, but there are at least short passages. For example the famous Old Irish hangover side note was written in ogham: https://www.tor.com/2015/01/28/medieval ... -hangover/

But true that it’s mostly the alphabet of very archaic stone monuments that predate the Old Irish period and shows visibly earlier stage of the language.

Dropping only happened in anglicized versions.