Is the Polish railway system very fragmented?

Actually there is no direct connection between Zgorzelec and Wroclaw, you will have to go from Zgorzelec to Wegliniec and there hop on a train to Wroclaw, both trains are operated by the same local railway company "Koleje Dolnoslaskie". (You can buy tickets here https://www.kolejedolnoslaskie.eu/en)

All of the polish railway companies (there is just a couple of them) are owned by the government and the http://rozklad-pkp.pl/ website is the best way to plan your journey. Just pick your start and destination locations and it will show all available connections. Sometimes it will require changing train operating company so for each leg of your ride you will need a different ticket.

Yes, there are several companies operating passenger trains in Poland. However, http://rozklad-pkp.pl/ should be a source of truth and cover all operators - redirecting you to the operator sites as necessary to book. For trips that involve multiple operators, you'll need to buy each leg as a seperate ticket from the respective operator.

For long distance trains, the vast majority are run by the national railway, PKP. Most regional train operators are government run. A few are private companies that some regions have contracted out to.

A couple of private companies are starting non-subsidized "open access" routes, competing with the existing railways. It's not clear to me if any of these are actually operating yet. They seem to be being allowed to start on rather niche routes.