You can find the network system requirements for the Slingbox PRO-HD here,
At the Slingbox location the upload speed should be at least 384 Kbps for Standard Definition (SD) and 1.5 Mbps to get High Definition (HD)
Back in Singapore where I stay have upload speeds of 3704 Kbps and download speeds of 1115 kpbs.
I recommend to confirm this numbers at speedtest.net and click on 'Begin Test', normally the download speed is faster than the upload speed
A) the maximum and the minimum upload and download internet speeds required to watch the program continuously without any buffeting or freezing of images with sound
It seems that remotely you will not have any inconvenience about the network, but at the Slingbox location, with 500kbps of upload, it will work okay.
B) for HD broadcast does the sling box need higher internet speeds.
That's correct, upload speed at home and download speed remotely of 1.5 Mbps at least.
Hope this helps