We purchased a 2.5" Seagate external hard drive. For power and data transfer it has a USB 3.0 cable, like this Amazon USB Cable. It works great on the USB 3.0 ports on the PC but the Smart TV does not deliver enough power through the USB port to work. I have tried it with a USB extension cable like this Powered USB Extender with an extra plug dedicated to power connected to a phone charger and it worked. I need that cable else were have the parts so i was looking to make a similar cable out of an old USB extension cable and a old phone charger. Would I be able to connect both the power coming directly from the port and the charger together or would I only be able to connect the power to the charger? I ask this because I also want to use the cable with other devices that do not require extra power.
Electrical – Make powered USB Cable for External hard-drive
chargerhddpowerusb
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It's very likely completely fine. You should be getting 5V on the non-PC end of the cable and your phone will limit current appropriately for charging. The only issue I can see is some companies will make cables proprietary by adding voltage dividers to the data pins, perhaps this is the resistance levels you're talking about? However, this will only mean your phone will not charge, it won't be damaged. This, of course, is all assuming the connector is correct.
What you are looking for is called a "USB Power Injector".
Many commercial (cheap) offerings exist. Here's an example. They are available in all USB connector types: A, B, mini-B, micro-B, etc.
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Here is the USB 3.0 cable pinout.
If you could somehow split out the 5V power/ground lines and connect them to an external power supply, I don't see why it wouldn't work. I don't think you should connect the signal ground to the power ground, but someone else more knowledgeable than me should weigh in on that.
I don't think the host would care if zero current is being drawn, as long as current draw stays under the max allowed. If for some reason it failed to detect the device, then you could add a dummy load resistor on the host side to fake it out.
Ensure data lines stay twisted and shielded to avoid signal degradation.