Hi,
As much as I understand from you: You have an old VM which you created in the old portal <https://manage.windowsazure.com/> (This is what we call a classic VM). The Classic VM you have uses a classic public IP which is a Reserved IP. You want to migrate the Classic Reserved IP to an ARM Static Publish IP.
Note! Unfortunately, I need to reproduce a scenario in order to test it and solve/confirm an issue, but the old portal redirect to the new portal for long time ago if you don’t have a classic service. The migration of the services to the "new" portal stared in 2015. As time pass it is getting much harder to find information about the Azure Classic and migration to the new ARM portal. At this time I do not have any account which have classic service (I might have option to work with the old classic in about 2 weeks since I have a call for support a client which might have it - don;t count on it). Therefore, I cannot reproduce a classic VM and/or Classic reserve IP at this time. This means that I can only provide old information without tests or confirm that it is accurate. I really do not want you to count on my memory from 2015 :-)
Anything that you do, is on your own responsibility. I think a better approach is to start from scretch and instead of migrating the Azure Services you can migrate your services (meaning create new VM and new STatic IP and configure your App there.
But read somewhere, one can convert a Reserved IP (Classic) to a Static IP, is that true? if so, how to do that
Yes it is supported as @TravisCragg-MSFT (Travis Cragg) mentioned already. You can migrate the classic Reserved IP to a Static Public IP.
I found this step-by-step explanation: (✅1️⃣)
if so, ... then can it be assigned to the new VM (ARM)?
Yes. After you finish to migrate the IP, then this part I covered in my blog (✅2️⃣). This step was tested and is done many times. Once you have Azure Static IP (after previous step) , then check my post. You have "Associate Existing Static IP to a new Virtual Machine" and you have "Associate Existing Static IP to Existing Virtual Machine"
Besides, creating a new Static IP and assign to Network Interface, does it mean, a new IP created with the desired Address?
No. New Static IP will get new address unless you migrate the old reserved IP. Check the link above to the step-by-step toturial.