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I intend to have mysite.com/keyword1.htm mysite.com/keyword2.htm etc.Is Google likely to show page keyword1.htm even if there are only links to my home page?
Yes, so long as your subpages feature those keywords in body text, title, etc. Exactly the same considerations apply as with your home page with respect to its keywords. And so long as the Googlebot can find your subpages, of course, with links from your home page.
All of the content on my site is in subpages, and most of my search-engine traffic goes directly to those pages. My home page is just an index page with a bit of introduction, and links to the other pages. It mainly serves to tie all the other pages together, announce what's new, and provide a convenient place for related sites to link to.
Is Google likely to show page keyword1.htm even if there are only links to my home page?
Yes, to a large extent Google considers a link to be a link, with no distinction between internal and external ones.
Like jtbell much of the traffic to my site comes straight to internal pages, almost none of which have any external links. But I have a good internal linking structure (a topic for another thread) which redistributes PR to where I want it to go.