Can you install amp and sub into a 2003 Ford Taurus?

Well I'm pretty sure you can but I noticed you have to buy the aftermarket raido kit for the car which is like 40$. And it includes the wires for heat and all that but just making sure I will be able to hook a custom head unit up to the wires inside the car?

There are two different questions here. Are you asking about installing an amp and sub, or about installing a replacement head unit? You don't necessarily need to replace the head unit to install the amp/sub.

Anyway, the correct kit for the vehicle will include the wiring to install the head unit. With the basic kit, the stock climate control switches just get detached from the back of the old unit and attached to the back of the mounting kit.

If your vehicle is equipped with digital, push-button climate controls instead of rotary knobs, you'll need a different kit which is typically much more expensive.

However, it's possible to install an amplifier and subwoofer without changing the stock radio.

You need wire harnesses for your new radio, no splicing and more because of the computer chips, or you have to hard wire it direct to the battery with a fuse in line.

So -- your title is amp/sub, but all you want to know about is the HU.
You can install an amp and sub w/o changing the HU.
And yes, you can replace the HU with the correct dash kit. The wiring harness is a little more of a hassle than most because you have to connect it to the radio control unit in the trunk and run it up to the dash, but it's not rocket surgery.

You can find some videos on youtube that might help.

I can in most imports, but I know you do not know what you are doing.

I can do it - but it sounds like you might want to take it to a qualified installer.

By the time you waste money on a kit to use your stock head end, you might as well invest in an aftermarket head end.