Because of the eclipse. Remember that a meaning "them" causes eclipse, where a meaning "it" either lenites or does nothing based on the gender of the noun.
Is it right to say 'ag fáil' as in 'I am getting new shoes today'? 'Táim ag fail bróga nua inniu'.
No. ag fail isn't generally used that way. You would generally say tá bróga nua á bhfáil agam, if you are getting them right now. If you will be getting them later today, that's what you'd actually say in Irish (unlike English, where you can use the present tense for an action that will happen in the near future) - beidh bróga nua á bhfáil agam inniu - "I will be getting new shoes today".
(ag fail is used in some circumstances, but it seems to have negative connotations - ag fáil bháis seems to crop up a lot!)
You don't, you say "he will be getting them tomorrow" - "beidh sé á bhfáil amárach".
I do say it that way and its understood and accepted by all those I speak to. My english has stood me in good stead for the past 71 years and I will hardly change it now. Anyway, thanks but no thanks.
I'm sorry, I wasn't commenting on your English (I say that in English too), I was explaining how you would say it in Irish, and why you would use "beidh" instead of "tá".