It can take a while for the site to be indexed by the search engines. There are a lot of things involved besides having a domain name.

Eventually, yes.
Sedo parked domains do get indexed by the major search engines. It could take some time before the search bots find it though.

Yes and No. The major search engines are not a fan of parked domains. I will mention a couple of things about parking, parking and sedo, and my experiences.

Since your domain will not have any content on Sedo Parking, it will never really rank high in search engines. Good content, backlinks from others sites, and a keyword rich domains are a few key factors to be ranked high. I must mention, there are some parking companies who do allow content with their parking pages.

Back to search engines not liking parked pages, I have seen many of my domains who were parked become banned by a search engine. My assumption was it was banned because it was parked because I was not doing anything with it. After about 80 days the domain received traffic again, which is the standard google ban period. Check out this site to see if any of your domains are banned:

Another tip relating to Sedo is they are known to pay very little for clicks. The main reason is because Sedo lets almost anyone park with them so the advertisers paying clicks pay out less because they know some of the Sedo traffic will be low quality or fraud clicks. Having said that, Sedo is a great parking company to start out with. You will learn a lot about parking through them.

Here is a list of parking companies for your domain. Each has their own benefit. I would be happy to help you choose one if you have any questions.