Learn English – It is still called your lap when you’re standing up

wash your mouth (out its soap)

can be said to children when they say naughty words and was a form of punishment to "wash" the filth out.

An adult version is

Do you kiss your mother with that mouth?

Your second phrase

watch your mouth
watch your language
watch what you say

can all be used in the same circumstances as "wash you mouth" and is a strong warning not to continue speaking in either the same way or in the same vein about something.

to watchout for what you say

I am an actual transgender person, so perhaps I should speak to this issue.

It is overwhelmingly preferred among my peers that the term transgender be used and that transgendered be avoided. I am a transgender woman.

The verb is transition: I have transitioned. Transgender is part of my identity, as is Asian and bisexual. We do not say I have Asianed or bisexualed, nor does this usage have any bearing on irrelevant nature/nurture arguments. I have not always considered myself bisexual, but there was no process by which I was modified to become bisexual. It is simply a term that best describes my identity at the time.

We call this identity-first language, and it is used because it emphasizes the membership of a person within a specific community. This is important, because it is, in North American culture at least, relevant that a person is transgender. Being transgender has a tremendous impact on how I exist in the world.

Therefore, we appropriately use the term transgender as an adjective within the community in a convergence with other communities moving to identity-first language. Transgender is not a verb that makes sense, so transgendered is nonsensical. And a transgender is also considered to be offensive and dehumanizing, as this usage strips us of our personhood, because of the power dynamics and sociopolitical nature of identity.

Calling me "a transgender" would erase both my personhood and my womanhood; it instantly casts me as an other, an anomaly, which further underscores the very real struggles transgender people experience in society. In this regard, "gay" and "lesbian" as nouns are the exception, not the rule. If anything, conceptual proximity of gender identity to sexual orientation has led people to assume that "a transgender" may be acceptable or even correct. It is not.

People who are not transgender (the term for this is cisgender) are not materially affected by the language used for transgender people, but transgender people are very much affected by the language used to describe us. For this reason, it is important to use the language that people within the community specify.