I'm afraid I'm bad at explaining phonetics :/ But this website is quite useful. As far as I remember, the 'ch' sound is pronounced in a weird way, it should be just like normal 'h'. And the rest shall be fine. Section two has some comparisons, that can be useful.
Also given the fact that you learned quite a lot of Russian, it's good to note that 'zima' is indeed pronounced differently there.
Aha! Yes, thanks! I should have known better. After teaching English as a second language for 6 years, bad student spelling and over-generalizing rules has messed me up. It also didn't help that I was doing my Polish lesson at 1 AM with 2 glasses of wine down the hatch already.