Apple TV and Air Play on 100/10 mbit speed

1/ The speed/bandwidth for your plan with your ISP is of no influence on your local home network, although one can be a limiting factor for the other. The connection between your Mac and the Apple TV box doesn’t involve the connection to internet and your ISP. Your home network speed will be limited by your router, switches, Wi-Fi, and/or ethernet cables. Home Sharing and AirPlay will buffer as much as is needed (and no more) for smooth playback.

2/ Indeed, the Apple TV box gets its content through the home network and sends it out through HDMI to the TV.

Your network speed is okay, however we do not know anything about the environment the Apple TV will be installed in. Without basics that include the home size, number of stories, number of Internet devices currently connected (phones, computers, tablets, tvs, alarm systems, lights, thermostats, locks etc......) it is difficult to judge if you will have adequate bandwidth where the Apple TV will be connected.

Apple TVs are streaming devices so your download speed is the critical factor. The minimum download sped to get 4K content is 15 mbs, the higher the download number the better you are. However if you have a large number of devices all vying for the signal that you affect how the Apple TV performs.

Your router will have a maximum wired speed that is hardware determined: gigabit (1000 Mbps), 100 Mbps, or 10 Mbps. (Or 10000 Mbps if you think you could use that.) Your devices will have a maximum wired speed that is hardware determined. Your cables may be rated for a certain maximum speed (Ethernet Cat 5e or later for gigabit). These are theoretical/marketing numbers, and real world speeds will be a bit lower. Simultaneous active devices on your home network will share the available bandwidth, each getting a part of the total.

Wi-Fi will likewise have an upper limit as determined by the router/WAP. Wi-Fi devices will have their own maximum. This is a bit more complex, as in involves Wi-Fi version compatibility, and number of antennas, and bundling those for a single connection where possible, as well as use of the 2.4 GHz band or 5 GHz band. Sharing the bandwidth with other devices will again lower what is available for each device. It also doesn’t have the neat factor 10 steps. Wireless interference may cause a lower speed.

For your specific setup and real world numbers, you can use speed tester applications.

Speedtest by Ookla (free) (macOS/iOS/tvOS/…) tests the speed that you actually get from the internet/your ISP, on the networked device. This then will include effects of your home network.

LAN speed tester apps (i.e. without internet measurements) may cost a bit, but there are several, if you Google for that. If you are confident that you can get more than 25 Mbps on each device, then you’ll be fine without measurements.