In such case, sitemap is still needed or not?

Let's not talk about "needed" but instead talk about "a good idea", OK? Regular navigation can create some very long click paths to inner urls. A sitemap makes sure you keep the click path pretty short - 3 clicks or even less.

Home Page > Sitemap > Sitemap 2nd level > Any url

Another good reason is that site navigation can get "fancy" -- graphics instead of test links, drop down menus, on and on. Many of these "nice things" may create spidering problems. Straight html sitemaps are a kind of insurance policy.

Also, the sitemap must be named as sitemap? Can it be other name like "directory"?

No reason I know of, except established standards. The more you break with convention, the more chance you lose something or someone along the way. "Sitemap" is a very clear communication, both to users and spiders.

Also, can sitemap have many pages or many levels?

Absoultely, especially if you go beyond 100 links or so on the page. It can be a very good idea, because you're communicating your site's structure to the search engines and mking the sitemap more usable for human visitors.

Also, sitemap must be in top bar?

Just a clear and obvious link will be fine for search engine spiders, although toward the top is a good idea especially if your template contains lots of links. Human visitors would probably expect to see "Sitemap" near the top right of the page -- but that's not universal, just common.

Must appear in every page?

Home Page alone can be enough especially if you don't think your human visitors will want to use it.

If have many sitemap pages, can it be named as sitemap-1.shtml, sitemap-2.shtml etc.....?

Or the root sitemap be named as sitemap.shtml, can the deeper level sitemap named as sitemap-l2.shtml, sitemap-l3.shtml etc..?

Thanks.

The file name will not matter. Use whatever helps you keep track.