no
No, homosexuality is not socially constructed. Sexual orientation is a natural and intrinsic part of an individual's identity and is not something that can be influenced or changed by society. Societal attitudes and norms may affect how individuals express their sexual orientation, but the orientation itself is not socially constructed.
Homosexuality does not affect your health in any way. Only unsafe sexual practices (of any orientation) can affect your health.
No. Sexual orientation doesn't affect insurance plans.
The character of Flapjack is not written with sexual orientation
Nothing is known of her sexual orientation.
The Joker's sexual orientation is not written into his character.
Soko's sexual orientation is heterosexual/straight.
I think you mistake "sexual orientation" with specific types of orientation. Sexual orientation is a part of every humans make up. A person can not have a sexual orientation. Your sexual orientation is what makes you gay, straight or bisexual. Homosexuality IS illegal in some countries. You can outlaw a behavior but you can't outlaw an urge or feeling.
The fictional character of Yoshi is not depicted with sexual orientation.
The sexual orientation of David Rodriguez is unknown.
Matt Evers' sexual orientation is not known.
The SNL character "Gilly" was not written with sexual orientation.