Melanie starts school tomorrow.

and

Melanie will start school tomorrow.

are both correct. However, it is very common using present to express future, so your first example is the more acceptable.

However, there is another problem I want to emphasize:

Melanie will start school from tomorrow.

is incorrect, because there is no match between start and from tomorrow:

• start: refers to a specific moment in time (defined or undefined);
• from tomorrow: refers to the period of time starting tomorrow.

So if you from "from", you get a correct sentence again.

Melanie starts school tomorrow.

and

Melanie will start school tomorrow.

are both correct. However, it is very common using present to express future, so your first example is the more acceptable.

However, there is another problem I want to emphasize:

Melanie will start school from tomorrow.

is incorrect, because there is no match between start and from tomorrow:

• start: refers to a specific moment in time (defined or undefined);
• from tomorrow: refers to the period of time starting tomorrow.

So if you remove "from", you get a correct sentence again.