TV only has USB 5V/0.5A and USB HDD 5V/1A? Is the 1A port USB 3.0?

I think the amperage limits are for devices pulling power. Just like a USB charger can supply 2A, your TV could be rated to supply more than the 0.5A that the spec requires. But it doesn't imply USB 3.0. You would have to check the manufacturer's specs.

You don't have a manual for your TV? Get one...
Your assumptions are basically right, and, fortunately, whatever you connect, it won't break, so you might simply try out.

USB 2.0 is 480Mbit. You don't need any higher speed interface.

To save you some confusion, there ARE nine contacts in a USB3 connector, as opposed to four in USB2. Interestingly, those extra contacts are used for the faster-data-rate signals, and not to supply the extra electrical power. But the point here is they do NOT look like "pins" as we often think of them, so you might not "see" them at first.

A common USB2 type A receptacle and connector has four flat metal contacts in a line near the front edge of a support plane. In the comparable USB3 socket the same front four are there, and then behind them are five more contacts. See this Wikipedia article

https://en.wikipedia.org/wiki/USB_3.0#Pinouts

and click on "Connectors" in the Contents box to leap down to diagrams and photos. Then you'll know what to look for in the USB sockets on your TV.

My GUESS is that Solandri has the right answer above. "Portable" hard drive units for use with laptops with only USB2 ports had a problem - none of them could actually work with only 0.5 A current available from a standard USB2 port. So they came two ways. One version came with an odd connection cable with two USB connectors on one end, and plugging both of those into separate standard USB2 ports gave the unit enough power to run. The other option was to supply a little power supply module ("wall wart") that you also had to plug into the HDD unit to give it the power it needed. The new USB3 units don't have that problem IF they are used with a real USB3 connecting cable and a real USB3 port that supplies the higher max current. BUT that means the their makers only supply with them a standard USB3 connecting cable and nothing else. Works just fine, until you plug it into a USB2 port. It will plug in and try to work, but normally it fails because the port can't supply all the current needed. You have to figure out how to give it the higher current required, even though you are only using the slower USB2 data transfer speed. My guess is that this is exactly what that special USB socket on your TV does - it is just a USB2 socket BUT it supplies the required 5 VDC at a non-standard higher max current of 1.0 A so that you CAN use the new USB3 "Laptop Portable Hard Drive" units with it. And as others have said above, the fact that is runs only at the older USB2 data rate does not matter for simply feeding data to a TV - that's not a very high data rate application.