This seems the perfect introduction for a very strange story :P "I know a cat that..."
Is there any rule, when first person singular suffix is -ę : widzę, noszę, mówię, lubię etc., and when alternatively it is -m: kocham, znam, jem, mam etc.
I think there are two ways of lerning it. You can either learn verb in infinitive , first person singular present, second or third person singular present and build from there like (like this http://www.skwierzyna.net/polishgrammar.pdf book says - page 44), or you can learn infinitive , which one of 18 tables it follows and the tables.
more about tables , and how to find conjugated forms https://www.duolingo.com/comment/13589661
Is that a case of 'connaître' and 'savoir' like in French and 'kennan' and 'wissen' in German?