Yes, a tv box is almost the same as a smart phone.
Yes, you can use universal remote control or even your other android phone to control your old phone.

To use an old smart phone to act as a tv box, there are 2 way
1. is cast the phone to your tv provide your tv has mirror feature. This method is a little technical because every time you want to use need to set the casting.
2. The other casting method is using usb to TV. There are usb cable to cast from your old hand phone to the tv. This method all you need is on the tv on the old phone which you could
leave it as it is without much effort.
However, unlike tv box which is built for such purpose and power directly which don't carried a battery, unlike old hand phone which does have a battery the old phone get heated up much faster.
Which mean your old hand phone life will be shorten faster and watch out not to over heat the phone.

As for software loading and apk, it does not matter too much between tv box and hand phone.

I have try it before, but i think with the cost of tv box or device which is so inexpensive, it is better you get a device specially built for such purpose.

A google chrome cast old version cost around $50 Sing dollar. A 4K version cost about $70

My suggestion is you get a device and the old hand phone use as a security device where you factory reset and installed your banking app and secure app and keep offline.
While your everyday phone can use as you like without the fear of being scam.
The old phone can then be online when need to use banking app and then set back to offline.

Hope the above help