Not exactly. 'Ithim' is a 'synthetic form,' combining ('synthesizing') the verb and pronoun into a single word; in the case of 'ithim,' that 'm' at the end is the first-person singular pronoun, 'mé,' which becomes simply 'm' when synthesized with the verb. The 'analytic' form (the form that keeps the verb and pronoun separate) is 'itheann mé.' That analytic form is more common in some dialects, but I have read that the synthetic form is the 'official' standard.
Same goes for the first-person plural: the synthetic form is 'ithimid;' the analytic form is 'itheann muid.'
Yes. Irish, like English, has a distinction between 'Paul eats bread (habitually, generally, etc)' and 'Paul is eating bread'. Some linguists even theorize that the English progressive developed from contact with the Celtic languages (I disagree with that analysis, though, as similar developments are found in non-standard dialects of other Germanic languages, so it seems to be a natural development). To say the latter you would say Tá Pól ag ithe aráin, using the genitive (literally translates to 'Paul is at eating of bread')
More a problem with my English and it being influenced by my native language, but anyway: is it really wrong to say "Paul eats a bread"? Admittedly I was thinking of "a slice of bread" as in colloquial German you can leave out the "slice of". But still, it could be a small bread and/or Paul being very hungry. So, is it really wrong to add the indefinite article? I mean in Irish we do not have one, so it could be in the English translation!?
There are very limited technical situations where an indefinite article can be applied to "bread" in English, and this isn't one of them. A native English speaker would not use "a bread" in this translation, and it would be very misleading to non-native speakers to allow such a translation.
Yes, when I thought a bit further about it after posting, I realized that I still had fallen for the same trap my German language roots had set up. You either have slices or loaves of bread in English, hardly just a bread. I would have edited my original post, but did not have a good opportunity until now. And editing it now might be confusing, so this will have to do.