Can I get around in Warsaw,Poland with only Ukrainian and some basic polish phrases?

You might have trouble, ukrainian is similar to russian and russian was Poland's second language during communist time, so some people who lived then should be able to speak Russian, mostly people in there 30s and up, some younger people do to. The basic Polish should help you to. So you should be able to get around but, with some difficulty. Try expanding your Polish as much as possible before going. You may have some difficulties in some situations more then others.