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Is there a way to explore shared PC files while connected (paired) via WiFi?
Use for example ES file explorer - it's free on Google play store. There is plenty of file managers capable of doing this.
I'm having a trouble connecting to my PC. My PC doesn't have a password, so I leave it blank but it does not connect. Is there a way to do this without using third-party apps?
You can't do it without third party app, because in stock ROM there is even no file browser . When you did not set password for you, you should give rights to share for guest user and (eventually) everyone and disable "password protected sharing" in Windows network and sharing center . Then from explorer you should use guest/anonymous option when you're connecting to windows share.