Bought new TV - should I plug cable line into back of TV or still have to use that 25 year old cable line?

I don't think you would get very many channels if you connect the coaxial cable directly into your TV. I think that is meant for connecting a digital antenna on newer TVs. You might get a few lower-numbered channels, but almost certainly none of the premium ones, as one of the things a cable box does is confirm which channels you are allowed to receive.

Yes, the cable line goes into the "in" connector on the box, and you connect an HDMI cable from the box to the TV. That's how most people, including myself, do it.

Hi, @MichaelDiggs! You ask a great question. We have filters in place that will not allow a customer to connect the coax cable to a TV and get any channels. This includes over the air channels/local channels. If you would like the TV to get over the air channels and not pay for an additional cable box you can pick up a digital converter or antenna, however you will not get any premier channels or cable in general.

It sounds like you have a cable box to use. If you decide to use that box, connect a coax cable from your cable wall outlet to the Cable In/RF In connection on your set-top box. Make sure this connection is finger tight. The HDMI goes from the box to the TV.

You do have a third option, you can use a Roku/Firestick to stream the Xfinity Stream App. Some TV’s have this app available or built in to your options. 

As noted, you typically cannot directly connect a TV anymore. Most areas have no analog channels, and most if not all digital channels are encrypted. About all you might get is a few public access channels.

Can I use the old cable i have from my cable box to my new xfinity x1 box

The cable itself should not make much of a difference if it's in good condition. Even the thinner/older RG59 is OK if it's just a few feet.