You can choose to have it added automatically (slower) or add it yourself. To add to Google, try this Add your URL to Google

If you want a counter which is good and real time. I wuld recommend Google Analytics, which is invisible. The other that shows number will be Stacounter. It is real time as well, even more precise than Analytics in terms of digging out details like users' browser types, screen resolutions, java enability and so on.

Good luck in blogging...

Well, to get others to add you easily, go out in hunt for link exchange. To go the harder but better way, blog good contents and people will link to you if they wanted to give a post long comment on your topic.

Try out Google webmaster to chech the last date when Google bots crawled your blog. Spiders travel through links.

Feedburner provide feeds reading, which such as email subscriptions of feeds (only contents) and reading feeds in readers.