JIt was just a couple of minutes ago.

If you want these first two sentences to be separate sentences, phrase it as per my correction. Else, if you want to have it in the same sentence, then you should combine them with a comma "Just a couple of minutes ago, my older sister [...]"

I felt a little bit impatient, she often asks me some basic questions and I don't [understand /know] why she doesn't [attempt/try] to search on the internet first.

Use either understand or know here.
Also I would have used try instead of attempt, but both are correct.

I really don't hopewant to answer her basic questions such as: "How to buy products online? "

or "Why does my smartphone cannot make a phone nowcall?

", and so on.

Anyway, she is always kind to me and willing to offer me help to me if I ask her.

Whilst I would still consider 'offer help to me' as correct, I would only ever write 'offer me help'.

A Phone Call from My Sister

Don’t capitalise every letter

Just a couple of minutes ago. I got a phone call.

My older sister phoned me and asked me how to find a program that hasd been installed on her computer.

I felt a little bit impatient, as she often asks me some basic questions and I don't understand know why she doesn't attempt to search on the internet first.

I tried to conceal my impatience andbut sounded dismissive while speaking with her.

I really don't hopewant to answer her basic questions such as: "How to buy products online? "

or "Why does my smartphone cannot make a phone call now?

", and so on.

Anyway, she is always kind to me and willing to offer help to me ifwhen I ask her.