Hello EBDECE
To play DVDs you need a device that can decode them. As far as I know, televisions cannot do this directly. You would need a DVD player or a PC connected to the TV.
To test the unit, check in File Explorer (if you have Windows installed) to see if you can see files on a CD and on a DVD. If so, the unit should be fine, but you will have a problem playing films (they cannot be decoded). Regarding the TV, as far as I know, the USB ports on all units are only for sticks (usually for firmware updates) or for hard drives (for recording). That would explain why it doesn't recognise the DVD drive.
What you can probably do with your TV is to "rip" the film (e.g. as .mkv), copy the file to a USB hard disk and then connect it to the TV. This should actually work with newer televisions.
I hope a specialist can confirm or correct my statements.
Yes, this is the device you need. It has always worked very well in my home. The USB cable is included and you can easily use it with your laptop. For the imac, no idea, Apple makes so many specialities so that their customers only buy from them...
Yes, according to the manufacturer's website, Windows 7 is also supported. See Specification -> Compatibility: http://www.liteonodd.com/en/dvd-external/item/dvdexternal/ebau108
PS: No additional drivers are required.
Since this is not a slot-in DVD drive, this should be possible in principle. With this drive, the DVD is inserted and held in the middle. Furthermore, a DVD is written or read from the inside to the outside.