Where is Jessica? I want to talk to (she/her). My brothers live in another city. I seldom visit (them/they). This is Mike. Do you know (him/he)? I am hungry. Give (I/me) some water. We're going running. Do you want to join (we/us)? I'm talking to you. Please, listen to (I/me). I don't know those girls. Do you know (they/them)? My best friend is very kind. I like (her/she). (I/Me) can't open this door. Can you help (I/me)?

Правильные варианты:

Where is Jessica? I want to talk to her.

My brothers live in another city. I seldom visit them.

This is Mike. Do you know him?

I am hungry. Give me some water.

We're going running. Do you want to join us?

I'm talking to you. Please, listen to me.

I don't know those girls. Do you know them?

My best friend is very kind. I like her.

I can't open this door. Can you help me?

Во всех этих предложениях после глагола или предлога нужен object pronoun, то есть объектное местоимение: me, him, her, us, them. Например: talk to her, visit them, know him, give me, join us, listen to me.

А в предложении I can't open this door местоимение стоит перед глаголом и является подлежащим, поэтому нужно I, а не me.