She didn’t notice and, continued walking and then stopped to look at some perfume.

A comma is used to list things. Use an ‘and’ to connect only the last two items in a list.

While she was looking at the stand, a random guy stood next to her,. He was looking at the same stand.

Reads better

She thought it was me and took his hand while saying something in Russian.

That guy was really surprised to say the least))).

My wife and I went shopping the other day.

It's better to say when this happened.

As we were walking alongdown an aisle, I stopped to check something on my phone.

Usually, you say "down the aisle" rather than "along the aisle".

She didn’t notice, and continued walking and t. Then, shen stopped to look at some perfume.

It's better to split the sentence up a bit with punctuation to make it flow better.

While she was looking at the standdisplay, a random guy came and stood next to her, looking at the same standthing.

In a shop you'd say "display" rather than "stand" usually.
I'd also add "came and" stood, because it shows he wasn't there before.

She thought it was me and took his hand, saying something in Russian.

I think this makes it sound better.

Thate guy was really surprised, to say the least)))

You're already introduced him so say "He" or "The guy" instead.
Usually "to say the least" is separated with a comma.