Question 1 No. However if you have a smart phone or tablet connected to the same home network, you can use it to locate YouTube content and in one click open YouTube on the HDR-1000S and replay on the TV.
Question 2 is unrelated, depending on your laptop, operating system and TV, there are a number of ways to view the screen and listen to the audio on your TV.
Direct hdmi/vga cable from laptop to TV
Screen casting from laptop to TV. In this case you would need a smart TV with miracast support an a PC with screen casting built in. Or a combination of usb plug in device on the laptop and a plug in HDMI device on the TV.