Seriously, you shouldn't feed bread to birds because they'll get aggressive when they try to surround you thinking that you're an unlimited supply of food. Besides, bread is bad for birds.
A bird eating bread not accepted. I'll assume my translation is incorrect.
"A bird eating bread" is a noun phrase where "eating" describes the bird's current action, independently of the main verb of the sentence. This description would use the "contemporary adverbial participle" form "jedząc." By contrast, in "ptak je chłeb," eating is the main action of the sentence, not just a description of the bird.
Because it can be :) For 99% of the Polish verbs, there is no difference between English Present Simple and Present Continuous.
This 1% are Verbs of Motion, and so-called 'habitual verbs'. Actually, there is a habitual verb "jadać" (Ptak jada chleb) which would render Present Simple here, but "Ptak je chleb" is also perfectly fine for "A bird eats bread".