1. ANT+ is definitely not going to work over 15m; signal strength of various sensors will vary but I get about 2-3m range without any dropouts. You could use a USB extender cable to get the dongle closer to your pain cave, but the max length for extender cables is 3-5m. However, you could theoretically daisy-chain a couple of USB hubs to make the full distance, but there is no guarantee it would work, because it's not what USB is designed to do. From the USB FAQ:
Q1: How long of a cable can I use to connect my device?
A1: In practice, the USB specification limits the length of a cable between full speed devices to 5 meters (a little under 16 feet 5 inches). For a low speed device the limit is 3 meters (9 feet 10 inches).
Q2: Why can't I use a cable longer than 3 or 5m?
A2: USB's electrical design doesn't allow it. When USB was designed, a decision was made to handle the propagation of electromagnetic fields on USB data lines in a way that limited the maximum length of a USB cable to something in the range of 4m. This method has a number of advantages and, since USB is intended for a desktop environment, the range limitations were deemed acceptable. If you're familiar with transmission line theory and want more detail on this topic, take a look at the USB signals section of the developers FAQ.
Q3: How far away from a PC can I put a USB device?
A3: With the maximum of 5 hubs connected with 5m cables and a 5m cable going to your full speed device, this will give you 30m of cable (see section 7.1.19 for details). With a low speed device, you will be able to get a range up to 27m, depending on how long the device's cable is. With a straightforward cable route, you will probably be able to reach out 25m or so from the PC.
Q4: I need to put a USB device X distance from my PC. What do I do?
A4: If X is less than 25m or so (see previous question), buy a bunch of hubs and connect them serially with 5m cables. If you need to go farther than that, put another PC, or maybe a laptop, out where you need the device to be and network it with the first PC using something that's intended to be a long-range connection, such as Ethernet or RS-485. If you need to use nothing but USB, consider using USB based Ethernet adapters to hook the PCs together.
Note that anything else operating on the 2.4 GHz frequency such as wifi, wireless speakers, or wireless mice will also decrease your ANT+ range.
There may be wireless ANT+ signal repeaters/extenders available but I did a quick search and didn't find anything immediately
2. If you know Apple TV will work to display Zwift on a remote TV wirelessly, I would get a second one - they're relatively inexpensive. Improve your Wifi signal in the garage by moving your router/base station, reducing interference, improving line-of-sight, changing the wireless frequency settings. Worst case you could buy another router and setting it up as a wifi repeater eg:
3. Not sure. It depends what you're using to get the signal to your TV. Does the Apple TV only replicate what's on the iMac screen? If you connect your TV to the iMac with an HDMI cable, you'll have the option of configuring the TV as a second monitor, so you can display apps on either monitor. But again you're going to run into run length issues; the max HDMI cable length is 50 feet or about 15 meters so that might be an option - but again there's no guarantee your iMac or the TV will support that cable run length, and you're going to have more cables running across your house.
Personally, it seems like a lot of work and hassle to create a setup that might not work that well in the end. You could buy an older PC gaming laptop on eBay for less than $500 for the garage, and have a vastly better experience.