I have a auto feed news website that get new posts from some other websites and publish in my website automatically.I want to know is it OK if I delete posts older than 6 months - 1 year or it will harm to website seo. beside I will redirect all 404 pages to Main page.
Question: Does Google/Bing and other search engines punish sites for removing old content?
No of course not. Search engines and users appreciate websites that are well-administrated and this includes purging, moderation, pruning, improving and creating new pages.
Question: Will I stop getting rewarded for the page if I remove it?
Yes, you can't be rewarded for something that no longer exists but that would be on the assumption that search engines are rewarding you for the page in the first place. Just because a page exists doesn't mean search engines value it, or consider it important.
You should try and avoid removing good pages that are useful, have lots of traffic or have reputable external signals such as social mentions, brand mentions and of course backlinks. If you want to start a new page again, under a new URL, then simply 301 redirect the old to new.
Question: If delete 6-12 months of content and redirect to the homepage will I keep my rankings?
Absolutely no... you will not keep your rankings with this method. Redirecting a user from Z to Y should always be relevant to what the user expects to find, taking a visitor somewhere else they might not expect is a bad experience for that user. Too many redirects to the homepage and then Google starts treating them as SOFT redirects which means they are completely ignored, they do not pass any signals or rankings. See: John Mueller from Google at 4 minute 52 mark where he talks about it.
404's does not imply your site is broken, its the right thing to do when you remove a page and don't have something equal to it. No search engine punishes for intended 404's.