Please try to give an extensive list, and be sincere. (A 4 year old!) And what are some tips on improving her grasp of English? My parents don't speak English at home, and I'm the only one that does speak it fluently, but I don't know what to do!

How are you today?
What is your name?
How old are you?
When is your birthday?
What day is it today?
Do you like to watch television?
What is your favourite television show?
What is your father's name?
What is your mother's name?
What color is your hair?
What if your favourite color?
How many brothers and sisters do you have?
What are you doing?
What do you like to do for fun?
What is your favourite food?
What is your favourite toy?


try teaching her colors, days of the week, and numbers (start small probably 1-20). she'll get the basics if you keep talking to her. recite english nursery rhymes and read to her using children's books in english. the memory is prone to learning things through song, so let her listen to a lot of English speaking music and television.
but for her sake, don't let her lose her native language either, she might blame you later if her only known language is English.

"hello."
"how are you?"
"What's your name?"
"How do you say___ in English" (ask in your language and have her reply in English)

etc
etc

little tip : when you ask a question, give your sister a normal sentence related to you to give her a sense of what you are talking about. She won't feel completly lost to begin with and this will boost her confidence as well. She'll look smart and she'll like that. Little by litlle you can then move on to just the questions so that she'll start to think in English totally by herself.

Good morning!
Hello!
My name is.......What is your name?
I am 15 years old. How old are you?
I live in London. Where do you live?
I have a sister. Do you have a sister?
I do NOT have a brother. Do you have a brother?
Do you like to play?
Do you like to play with dolls?
I like to eat dessert. Do you like to eat dessert?
I prefer chocolate. Which dessert do you prefer?
Did you sleep well?
I am hungry. I want to eat an apple.
Are you hungry? Do you want an apple?
I am thirsty? Are you thirsty?
Let's play!
Let's go for a walk!
Do you want to go to the park? to the palyground? to bed?
Good night! Sleep well!
Thank you
Please
May I....?
Can I .....?

These are just a few.

Puzzles - the wooden kind or other types -are also a great way to teach/learn a new language (the farm, the animals, household items, etc...).
Sing nglish songs and mime them while singing.
Everytime you pick up an object, a toy, a piece of clothing, kitchen stuff tell her the name of it.
Let her first answer with single words and slowly graduate to a fuller sentence using the words of your question and putting them into a affirmative/negative sentence.
Keep it simple and interesting to start with. She'll quickly catch on.
Hope this helps.

Good for you! At 4, I think if you just talk to her, she'll absorb English like a sponge and grow up to be bilingual.

How old are you? (Tell her to ask how old you are.)
What's your name? I didn't hear you. What did you say?
Where's the blue ball? Show me the blue ball!
Where's the little ball? Show me the little ball!
What's your favorite TV show?
Who's on the show? What are their names?
And what do they do on TV?
What color is the [something in the room]?
What a pretty dress/shirt! What pretty shoes/pants! What color are they?
What do you like to eat?
Where are the clouds? Aren't they pretty!
What's it like outside? Is it raining? Is it hot out today?

That's what's great with kids. You can ask all kinds of dumb questions, and they don't really care! You can play pretend (shiver as though you're cold, jump up and down and ask her what you're doing, etc.). Stuff like that. What she's wearing is always a good topic. Her favorite toy or doll.

Oh ok... When you start, ask questions that are yes and no and to start her off, say your answer too so she gets and idea of whats going on. Then quickly move on the questions with an opinion so there is no wrong answer, and then move on to fact questions.... Tips? Always speak to her in English so she will start to think it as well. Thats all i can tell you!! i would ask her simple questions like these:

What is your name?

How old are you?

What color do you like?

What's MY name?

Name your fav animal.

Are you hungry?

Are you thirsty?

Whens your b-day? (idk if shed know that)

Where do you live?

How are you feeling?

Are you upset/happy/sad/frustrated/etc?

Where is mommy/daddy?

Do you have any sisters?

Do you have any brothers?

What is your favorite toy?

What do you want to do?

Can you show me a lamp/tv/candle/paper?
(questions like these will encourage her to think and name things)

Good luck and let me know how it goes! God Bless....!!

You may try to introduce her to Kids english cartoons or programs. Kids music also, kids learn while having fun. Also try toys in english.

Questions:

What's your name?
How old are you?
What color is this?
Do you like this?
What's this? (mayb point a chair, an animal, a plant)
What letter is this?
What food is this?
What would you like to eat? Or do you want to eat this?

Star with basic words.