Ask HN: Can ISP see what you're doing through a proxy server?

If I use an IP:Port proxy server to connect to the internet, I'm aware that the destination server (website) doesn't exactly know it's me, but can my ISP know what site I went to?

What would an ISP see if I connect to the internet through a proxy server I've set up on ec2 or something?

Lastly, if my ISP can actually see what I'm doing, is there a way to hide from them (e.g. does connecting through an HTTPS proxy hide what I do)?

Thanks!