元気を出して

なみだ

tear; tears; crying; sympathy

Watching the sad movie, I couldn't stop my tears.

Refers to the liquid secreted by the eyes, but also figuratively to the act of crying or feeling sympathy.

and so on, et cetera, and the like; things like

I read books, magazines, and so on.

など indicates that the items mentioned are examples and there are other similar things not listed. Often follows a list connected with や or と. Can also express humility or downplay something when referring to oneself (私など 'someone like me'). なんか is a more casual variant.

みせる

to show, to display

Please show me the new photos.

見せる is the transitive form of 見る (to see). It means to show something to someone, making it visible or available for viewing. Often used with て-form for polite requests.

つよき

confident, bullish, aggressive

He surprised everyone with his confident remarks.

Describes a strong, positive, or assertive attitude. Often used in contrast to 'weak' (弱気).

copula particle for na-adjectives; negative imperative particle

Study in a quiet place.

な connects na-adjectives to nouns they modify. It's the attributive form of だ/です. Also used as negative imperative particle meaning 'don't' after dictionary form verbs.

you (polite)

Please tell me your name.

あなた is a polite second-person pronoun 'you', but often avoided in favor of names/titles. Between spouses, wives may call husbands あなた (similar to 'dear'). Can sound distant or rude if overused. Better to use name+さん when possible.

direct object marker particle

I solved a difficult problem.

Marks the direct object of a verb - what the action is done to. Written を but pronounced 'o'. Essential for transitive verbs. Also marks the space through which movement occurs.

so much; that much; (with negative) not that much

Did you study until that late at night?

Used to indicate a high degree of something. Often used with a negative verb to mean 'not so much'.