Cultural difference make me confused. Is it out of line?

i think its a right thing to do. u only want to do her some good and wants to help her. just poplin with the food and give your regards as a new neighbour.

Hello rose1chae,

Perhaps you can make the food you plan to make and say to the lady downstairs, "Here is dish of food I made for you.  I do not mean to invade your privacy, I just want to express two things: one is to welcome you to the neighborhood (and I am a new here too), and the second is to wish you get well wishes." 

If the conversation takes off from there, you might want to mention your work back ground as a nurse, and that if she ever needs help to call you. 

One of the first things I try do as a new person in a neighborhood is to find the right time to introduce myself to each of the neighbors and do my best to exchange phone numbers. 

I explain to them to feel free to call me should they need help or for any reason. Some times it works out fine, and other times they look at me like I am speaking a different language - LOL. 

I the main thing to remember for some one like you who has such a great heart is if it does NOT go smoothly, do not take it personally.  Every one responds differently and it really is their issue and, and not you as a person. Does that make sense.

GOOD LUCK!!
Regards, LAN

Hi Petaluma
Thank your for your kind comment!! I will keep in my mind.
I agree that your opinion. Responding is very differently and case by case depend on their nationality, background and experiences.
First of all, I wrote a letter such as my background, just want to say " hello" " nice to me you"
I do not want to invade your private. I have had never any illegal violation took medications.
If i receive reply about my asking, I will prepare food as next step.
if she doesn't want it, I will respect her opinion.