Welcome to the wonderful world of Tridion... Get ready to go through this cycle a few times in the coming months.
Here's a couple of examples to achieve some of what you're searching for - but not all. Tridion does not store the information you're searching for in the CM, it's only available in Content Delivery - unless you want to do some date comparisons.
First, the basics - read a Component:
var c = (ComponentData)client.Read("tcm:1-2", new ReadOptions());
Read a Component's Version Info:
FullVersionInfo info = (FullVersionInfo)c.VersionInfo;
int currentVersion = info.LastVersion.GetValueOrDefault();
Finding out publishing information about the object involves asking Tridion for some more advanced system data, which is not directly part of the object. In particular, you will want to look at PublishInfoData:
foreach (PublishInfoData p in _client.GetListPublishInfo("tcm:1-2"))
{
Console.WriteLine("Item was published at {0} to target {1} rendered with {2}",
p.PublishedAt.ToShortDateString(),
p.PublicationTarget.Title,
p.RenderedWith.Title);
}
Have fun, and come back with more questions.