reducing the halting problem to the blank tape problem I have checked many discussions for understanding this problem.

I understand the reasoning , unfortunately there are some drawback in my understanding.

The Blank-tape halting Problem

Input: Turing Machine M

Question : Does M halt when started with a blank tape?

So this is the reduction :



The construction of Mw is as follows :


When started on blank tape, writes w 
Then continues execution like M


What i don't undesstand is the step 2 , in my opinion if we execute M on w maybe M will loop !!!

My second question : what the blank-tape do when executed?even if the blanktape machine halt on blank tape , how can we be sure that M halt on w .i miss something here.

Thank you in advance.
The reduction does not actually execute $M$, what its actually doing is the following mapping:

$\big(\langle M\rangle,w\big)\mapsto \langle M_w\rangle$

Where $M_w$ is the machine that when executed with blank tape, simulates the machine $M$ on input $w$. Preforming the reduction does not require that you execute $M$, you simply need to write down the code of $M_w$. Obviously $M$ halts on $w$ iff $M_w$ halts when executed with blank tape (we constructed $M_w$ specifically for this purpose), and the correctness of the reduction follows.