Bondi:
while I go on and say “czy” or “poczebuję”, native speakers tend to say “t-szy”, “pot-szebuje” etc.
If you live in Poznań you can achieve a full assimilation with the local folks, most of them say "czy" (for trzy), "czeba" (for "trzeba") etc.
To sound more local you also have to make voiced consonants at the end of the word before another word beginning with a voiced consonant (for example: jak nie in Poznań is usually pronounce as "jag nie").
And learn the specific intonation in the questions.