I have PR 4 website with thousands of pages individual pages have 0 PR. Does the website domain page rank (which is 4) effect the pages?
IMO It can if your internal linking structure is set up right - It wouldn't do much for each page if your homepage's PR was spread out amongst all of your pages plus linking out to other sites. Get some good deep links and try linking to less pages from your homepage (assuming you link to a lot). If you have thousands of links on your homepage it decreases the amount of "PR juice" that each link can pass to a different page.
On my homepage, I have a internal link list of 30 random articles to help the bot crawling. Is it any bad?
the more links you have from your main page to your other pages, the more pagerank tah pages will get
home page rank always effects the pr of those pages which are having links on homepage but try to keep minimum links on homepage
In short - no. Technically it doesn't affect it at all. However, as others have said, you're likely to have a lot of links from your home page to your inner pages. Those links will spread some PR to those inner pages. I would recommend nofollowing those links. Having them on the page might not be bad from a usability standpoint, so they're worth keeping. However, nofollow them and then direct the PageRank through a more static structure so you can get more consistent link juice flowing through your site. "More" PageRank? No, it's the same total amount, but becomes less per page if you have more outgoing links. If you link to one page, it gets 100% of the outgoing. If you link to two pages, they each get 50%. If you link to 100, they each get 1%. You should also look at doing some siloing. Put nofollow on useless pages (privacy policy, log-in, etc) so that you can keep the link juice flowing the content pages that you want to see ranked well.