need 13 outputs from arduino uno

I'm working on a project that requires thirteen outputs (LEDs and a push-button), and I was wondering, is there any way to turn the analog pins or pins #1 and 0 (TX and RX, respectively) into regular digital output pins?

Yes to everything. The analog pins work as digital, if you address them as 14, 15 ..., ie digitalWrite(14) will output on analog 0. (Remember to set pinMode() first, of course)

pin 0 and 1 work fine as digital pins ... as long as you do not use the USB or Serial stuff. Usually they are not used as plain digital pins.

Awesome, thanks a lot!

as long as you do not use the USB or Serial stuff.

As that includes uploading a sketch it is quite difficult not to use them. You can always switch out those pins when doing the uploading like I did on this project:-
http://www.thebox.myzen.co.uk/Hardware/MIDI_Shield.html