I've been asked to create a platform that broadcast video live but I have many questions about this.
Thank your guys!
I would like to build it with PHP, using Laravel for the backend and AngularJS for the front end. Is this a good idea?
I've used Laravel and Angular in conjunction and it works fine, there are plenty of resources on the net that can help
Are there any services already built that I could integrate to my application so the video broadcast goes to them but show it using their resources but viewing from my Laravel App?
Yes there are many. Brightcove and Livestream (as well as many others) offer video transcoding and players that can be embedded in the websites. I can't recommend one over the other, ive used brightcove in the past but not for livestreaming
If there is no services I could "plug in" to my app, what does it implies to develop this technology?
It implies a lot. You'll need some way to upload the video streams, transcode them on the fly, and then figure out how to distribute them to the end users. It's possible, but I wouldn't recommend it. If you have to go that route I know AWS offers a few services that might help such as Transcoding as a Service as well as live streaming from the Cloudfront CDN.
Edit: Wowza is another service I've played around with that might be worth looking at. Kinda a mix between rolling your own and going with a completely managed service