All these features and more are available in Opera Mail (M2, not the web portal).

It has a single unified Inbox for all mail, has filters ala gmail, and filters based on message body. Additionally, each folder can also be filtered out temporarily by date. Thus you can shortlist out emails that you received in a day, last 3 days, last week, etc.. (This is similar to the feature that Outlook has, but better). Its pretty fast, and with the new Opera 9.5 release, there are a lot of improvements to the mail client. And of course you don't have to pay a dime for it. I have been using for close to 2-3 years now, and use it to maintain a reasonable number of mails ~500MB worth. It does bayesian filtering for junk mails. You can create folders where the bayesian filter learns on the basis of the emails that you put into it.. And in true Opera tradition, its stable and fast!

I'm not sure why its not advertised enough, but its got all the features of thunderbird and outlook. What it lacks severely though is calendaring.