Is there any manga in which the female lead protects the male lead. The male lead falls for the girl but is annoyed by the fact that he's a weakling and the girl has to protect the guy.

Or, a manga where the girl takes care of the guy but actually he can take care of himself but acts babyish in front of the girl to get attention. Example- 17-sai kiss to dilemma, ouji sama ni wa doku ga aru.

Try Fushigi no Maria-kun.

Mugen Sowaka - Toukyou Shoujo Onmyouji

I would also recommend the Female Bodyguard category tag.

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Nulla in mundo pax sincera
"Always go too far, because that's where you'll find the truth." - Albert Camus

SP x Baby. A light, breezy read that'll be fun if you're not too concerned about shoujo cliches and nonsensical plot development.

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mostly angry, always witty

9 Banme no Musashi
Tokyo Crazy Paradise

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<b><span style='color:#FA8072'>Chinese Translator</span></b> <BR><BR><span style='color:#32CD32'>Accepting translation requests if the manga interests me!</span><BR><BR><!--url_type_2--><a href='http://www.sephiria-chronos.tumblr.com/' target='_blank'><u><!--img--><img src='http://i.imgur.com/uyTyBbB.png' border='0' alt='User Posted Image'><!--img_end--></u></a><!--url_type_2_end-->

The main guy is nothing like your requirements, but he does like female lead first (and possessive, which is yum): Grand Sun. I second SP x Baby, definitely fits some of your requirements for the male lead.

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I'm in idol hell T.T