"We run today."
So, one does not have to use the first person plural conjugation? Can one also use this conjugation for the first person singular?
Yes. You don't always have to use the -(a)imid ending. That's called the synthetic form of the verb and is really only used in Munster and the Standard. In Donegal or Connacht you'll likely here ritheann muid.
In general, only the "synthetic" version of the first person singular (the version that has the pronoun contracted into it) is used - for example, rithim, ólaim. The non-contracted version, ritheann mé, is not standard Irish; it is used in one or two very local dialects but to many people's ears it would sounds unnatural.
The verb bí is an exception: both tá mé and táim are commonly used, and both are included in the official standard.
Some internal consistency would be nice. Everywhere up to this point, it's been Rithimid, and now you throw in Ritheann muid?
For all verbs in the present tense, either the -(a)imid ending or the -(e)ann muid ending may be used.
While that's great, and believe me it is because I learned it a muid, every example in the system barring the first introduction (and even then only in the overview page at the start) uses Ithimid which doesn't lead you to believe that you can use muid. Hence it's setting people up for failure when you suddenly show it many exercises later in a multiple choice round.
I tempted to agree, but the only time it's going to bite you is in multiple choice (and hopefully then only once), and it prompts people to understand the evolution of a language with three very present dialects a bit better. Then again, I may just be an apologist based upon some of the things thrown at me in the French course. ("But we haven't even learned past tense yet!") ;)
Well, in a classroom setting, I would definitely agree with you. Here though (and in immersion classrooms) we are left to decide for ourselves what is going on. I suppose some sort of clear explanation of the dialects in the "tips and notes" might work though. I have been trying to think about whether this is a problem unique to Irish, since I have always been taught only one dialect of a language, though a teacher may have mentioned offhand that they say it another way in some other area. I know that, for instance, one learns Brazilian Portuguese or Continental, Egyptian Arabic or Lebanese, Maghrebi, Gulf, etc. When I was learning French, I can remember being fascinated by my teacher telling me about Swiss, Canadian, African, and other variations, but what we were taught was limited quite definitely to Metropolitan, even Parisian French. Do they try to teach British and American English at the same time? Good Lord, I hope they don't try to throw Australianisms in.
When I learned ancient Greek, we started with one dialect then eventually learned the variations present in others, in large part because a character was introduced who spoke with a different dialect. (It was also when simplified passages from an ancient historian who wrote in that dialect started to be introduced.) It was definitely a bit odd switching dialect's like that, but, at least for ancient Greek, it was beneficial, given that classical literature can be written in any of four dialects (including Homeric, which was basically the others squished together with a few additional variations to make words fit the meter more easily and was never actually spoken in non-literary common use).
It is, however, a great way to forget how to spell things. :)