I am from Ireland and I live in the mountains in Poland, not as far as Zakopane. There are many many treks, some better than others. The thing I do not like about the main stream treks in Zakopane is that there are far too many people on the path (directly infront and behind you) but do not worry there are plenty of treks.
Is it easy to hike on your own in the mountains, I heard that there are colour coded walks,
Yes, it is very easy. Some routes are dangerous especially at certain times of the year, nameingly winter. Go alone you will be fine. I have no idea about tours.
You will be fine, if there is anythig more I can help you with do not hesitate to ask.