programming a ATtiny85 using Arduino UNO

When programming the ATtiny85 using UNO can the ports tied to UNO to the tiny85 be programmed to perform I/O after programming is finished and downloaded and after turning off power and disconnecting the UNO from the tiny85 then applying power again?

Yes. Once your sketch is running all the IO pins are controlled by it.

Other stuff you may not know that should be useful to you real soon:

Re-moding IO pins to act differently on-the-fly at run time is behind quite a few Arduino tricks.

Pins can be in 4 different states electrically:

OUTPUT and LOW will sink up to 40mA current for very short periods or 20-25mA continuous/
OUTPUT and HIGH will source the same as LOW will sink.
You have to make sure that limits do not get exceeded. Usually current-limiting resistors are used.

INPUT and LOW will only 'eat' 1 millionth of an amp when the pin is read. But you can read it very fast.
If you don't read an INPUT LOW pin. it will be electrically neutral.
INPUT and HIGH will source a weak current. You can ground the pin safely with no external resistor.
This is great for buttons/switches. It's ground-safe and needs no external pullup or pulldown circuit.

MIT ATtiny programming in case you don't have this link.

I don't see how you would do it any other way. It'd be kind of pointless if you couldn't use them.
Only caveat is the reset pin, which you should leave alone, unless you know what you're doing.