A) Sila:-

1. To invite/ask people to get enter in the house.

Ex: Silakan masuk (Please, c<em>ome in</em>)

2. The way to sit on the floor (bersila)

3. Ask someone to do something

Ex: Sila lengkapkan ayat di bawah (<em>Please complete </em><em>the sentence below</em>)

B) Tolong:-

1. When ordering something. (Change <em>tolong</em> to <em>minta</em>)

Ex: "Minta kopi dua" (<em>Two coffee please</em>)

"Minta satu lagi pinggan" (<em>Could you please bring me an extra plate</em>)

"Minta mi satu" (<em>Noodles please</em>)

2. Used as a request or plea for assistance.

3. Reminder to someone

 Tolong and sila can be used interchangebly but 'tolong' can put more tense on the sentences where else 'sila' is more polite. both means 'please'. 

But tolong is also another word for 'help'. example tolong saya, 'help me', or tolong orang itu, 'help that person'. In your example above 'Tolong mi' is not right because that literraly means 'help noodle'. sila mi also cannot be used. a more subtle way is just to say, 'silakan' (while the meal is being served to that person). 

I suggest that you just use 'sila' for polite request (please) and use 'tolong' exclusively for the word 'help' to avoide confusion. Then slowly use 'Tolong' when you want to put more emphasize and tense on your request. 

"Sila" can be used to politely requesting or giving instruction someone to do something, eg.
Please que up (Sila Beratur). And in this situation, "Sila" and "Tolong" can both be used.

And yes, the correct definition of tolong is to plea for assistance.

Tolong saya dengan masalah ini = Can you help me with this problem .
In this situation tolong can be translated into the word Help, and CANNOT be subsituted with Sila

sila: please

tolong: help