If the client says the logo must appear on all the company screens, even those of the mobile application, of course he's in his right to say that and is absolutely correct.
But, this is where the professionalism of a graphic designer comes: for this situation there are design variables in a corporate image. Nowadays a logo is not simply the image of the ...
I'm afraid that there will be always be stakeholders who overrule you. If they say it's a must, there's not much you can do about it.
That being said, your number one reason (it would consume screen space) is a fair one. Especially on mobile devices, the limited screen space needs to be considered. Try to back your arguments with examples of other apps or ...
In general I'd recommend to be careful with trying to do something new in this area, unless it's absolutely tested and user(fool)prove. You got to be very careful about this - I see the danger of confusing and especially prospects and thus loosing them. The standard expectation of users imho is that Registration and Login are two different processes.
I believe when the user clicks on the button save and the second block is empty, don't need validation because it's not a priority for the user the fields empty. If he clicks on the button accidentally he can finish the task and if he needed the second block and forgot, he can edit this information later.
Save button on the bottom. The flow should follow natural behaviour. The user will click on the save button after filling the form and then naturally the action should be there, after form. But if you not confident about this, please add both, on the top and on the bottom.
You could create 2 stages of verification:
If any data was filled on ...
You could preform a test without the onboarding and see where users struggle.
With this info you could make your onboarding process better.
With this new onboarding you can make a new test and see if the users understand the new feature instantly.
This way you tested your feature and the onboarding.
If feels like you should. Sometimes complex, or even just new features have to be explained. This is called onboarding.
The secret is whether the new feature is ultimately usable. Ideally, this would be without any kind of explanation: 'a perfect system'. But often this is not the case, so a degree of explaining is needed to ensure the new features are ...