I'm new here.Will the rank make limitations on posting or can I post just like the higher ranking one except for the wait time, avatar, signature, and tags?
You can make as much post as you want (respecting the waiting time of course), to avoid being banned for spamming, try to stick to the subject and make constructive posts.
Signature grows with your rank, avatar is available for full member and higher ranks.
If I want to make an announcement for a new project or launch a bounty campaign, will the new account do some influence on that?
You can make announcements for ico and other projects whatever your rank is. The only influence is that images can't show until you become junior member... (And some people don't trust newbies so much)