'czy mogę ma rachunek proszę' is better
chaza objectivly speaking this sentence could be pretty hard to decipher for a Polish person out of context - used in this specific restaurant setting it would be understood what you mean - the main thing is rachunek here and mogę also helps - so you would end up with that bill you requested
the implication here are it is good/helpful to have lot's of vocabulary (like rachunek)
the grammatical forms of nouns are not so important, nouns in basic forms are nearly as informative as the declined forms
it is helpful to know most important forms of the most important verbs like the verb móc(móc is an infintive of course) - in the most important forms I would include the present tense personal forms (like the first person form you used) but also the infinitive
you can stick to the infinitive (basic dicitonary) form for other verbs - cause it is pretty difficult to keep track of all those conjugation patterns for a start
learning to deal with the aspect of Polish verbs (the perfective and imperfective in short) seems to be pretty difficult and it is not absolutely necassary for a rugged communication
it is very useful to know the most important prepositions and pronouns and their forms - like ja,ty, tobie , ciebie, im, wy, was, pod, nad, do, od, przy, z, o, za
there is not so many of basic pronouns and their forms an they are a nice introduction to the world of cases
as for prepositions - it is a wild and quite vast area - they oftentimes don't work the same as in English and it helps to know what preposition should be used in a given situation - there is also this thing that some phrases English that make use of prepositions have Polish counterparts without any (by car - samochodem) (this is an importan Instrumental case of nouns which generally translates into English as 'with the use of 'a noun')