ONiel

Use could use the pen tool to make a curve that follows the shape by importing the image and tracing over it. Another way to do this is to use the shape tools such as the tear tool and the crescent tool. The crescent tool is used to make the smile and the ear tool to make the tongue and tear shapes. You then modify them using the shapes adjustment nodes (red dots)

For the 3D-mockup, I wouldn't reinvent the wheel in this case. There are a tons of good (photoshop) mockups for this motive available. Fully customisable and quite a bunch of them for free. Since the display is flat, those mockups should work in Affinity as there shouldn't be any warping involved. Affinity can't render photoshop mockups which include warped (smart)objects.

I took your design into the Pixel Persona, then using the selection brush, created a selection on the inside of the cellphone. Masked it. I didn't do this, but you could put a Outershadow on the cellphone.

mobile_bon_on_iphonemasked.afdesign

Oh yes, there is still the matte option, and it seems the current term for including whatever is under the selection boundary box (the former "Selection with background") is now "Selection Area":

Anyway, the selection that gets exported is not what most users would expect, when using masks or clipped object. 
EDIT: What one would expect is of course subjective and determined on what one is used to: in CorelDRAW the exported (PNG) selections are defined by the actual clipping mask, not the clipped object(s), but e.g. in Illustrator both the clipping shape and the clipped object(s) together determine the export bounding box. 
EDIT2: The only way to have cropped export without rasterizing (and not including the boundary boxes of shapes used for masking) that I can think of is creating an artboard (and if necessary move the art to be exported onto the newly created artboard), and then manually size the artboard so that it accurately encloses the art. After that choosing just the specific artboard as the source of export would give a file without whitespace on edges. 

In the "More"-option in the export dialoque you can choose the backround color. Defaul is set to 'none'.

Yes, there are multiple issues:
1) Designer (or any oher Affinity app) cannot export accurately a selection that is masked or clipped, but instead, if an object is masked (as in OP's example), the object boundaries of the masked shape will determine the export size (in this case the line extends to left and right of the mask so there would be extra padding on left and right):

or if it is clipped, the clipping shape determines the export size in this case there would be extra padding at top and bottom according to the clipping rectangle's height):

This means in practice that the selection to be exported needs to be rasterized before exporting to be exported exactly to the desired effective bounding box where pixels will be rendered:


2) In addition: if the canvas is smaller than the exported selection, the parts that go beyond the canvas will not be rendered but cause transparent padding, so to fix this specific case, the canvas should first be expanded and then the selection be rasterized and exported as a selection only after that. A necessity to do that is truly annoying.
3) Last, it seems that Affinity has removed the user's possibility to choose whether selections are exported to PNG with or without a background. At least in 1.8.5 versions this option still existed but not in current release versions. So currently PNG selections will always have a transparent background, also in paletted versions. [EDIT: In current version this option is titled "Selection Area".]

What exactly do you have you selected?
I ask because in your afdesign file I see only a curve (the line) with a rectangle nested in it. So whichever one I select, in the AD export PNG dialog the only choices for Area are "Whole Document," "Selection Area," & "Selection Only." There is no "Export selection without background" option for me.

support-button.afdesign You can easily draw that as plain vectors, which has the advantage that you can scale it up/down as desired.
1. I started with the phone inside a speech bubble on a rounded rect ...
draw an equal sized green rounded rect use an Affinity speech bubble shape, set white stroke color and no fill color use the Glyph browser and find a phone in some glyph text font, set it to white color and afterwards convert it into curves place the speech bubble and phone curve on the green rounded rect and arrange or center them on that group the whole and name that group "phone-part" 2. Next choose some matching font and type the SUPPORT text and also add the red filled circle ...
then select and arrange the "phone-part", support-text and red-circle (center them all together vertically) group those all together named as "inner-parts" 3. Draw the white rounded rect ...
place the "inner-parts" group onto the white rounded rect and arrange (center horizontally/vertically) now group the white rounded rect together with the "inner-parts" for example named as "support button" 4. If you want add a black rect as a background to the document at the bottom of the layers panel, which you can toggle on/off on demand
5. You've done!
 

Nice 👍

Looks good @ONiel and your welcome.

@firstdefence First of all I want to thank you a thousand times for your help. That looks amazing.
Not having a tool to change the perspective in a designer-tool sucks to be honest. Now I really need to buy a whole other software-package only to change the perspective?
 
 
This is the result as it will be used on my site:
 

Affinity Designer doesn't access Affinity Photo if an Affinity Photo specific filter is used, it is a self-contained file. I tried this by password protecting Affinity Photo and if it had tried to gain access it would have triggered the request for a password.
I begs the question, why is this filter/tool not in Affinity Designer. 

Just out of curiosity, I wonder if it's possible if you only own Designer, to open a file originally created in Photo that uses the live perspective distortion and have access to the settings -  if so you could always drag the layer to your assets panel and always have access? in theory?
I can't test this as I already have Photo but I've created a photo document with a group that contains a vector square and a live perspective filter (Latest Photo Beta) just wondering if someone who only has Designer could test? although I guess it will have to be latest Designer beta : see attached
Perspective test.afphoto

The obvious way would be to group all items and grab one of the corner nodes and drag to create perspective - this was one of the first pitfalls I came across with Designer back in 2014, as it's just a standard, basic feature of a pro vector application, at first I thought it was some weird bug, but as it turned out, Designer didn't have that capability -YET- but was planned for a future update - wow - me thinking it may be two or even three years down the line before I can work comfortably ------ keep faith ------- 6 years later - no mention of when we'll get this - the road map was buried years ago - and vector distortions blanked - my faith is on fumes - well that's enough negativity, in the meantime, as firstdefence suggested 

You have to select the Background layer from the Layers panel first.

There is no active object to get cropped in your video. To have an object activated do either/or...
– single-click on the canvas before dragging
– click on the layer in the layers panel to select it

Select the image File > Export Export Options: Area: Selection with or without background

You can customize the tools panel and the top button bar via menu entries under the view menu. (View > Customize tools etc.)

Hello ONiel and welcome to the Affinity forums🙂
If you’ve not already found it I can highly recommend you check out BetterTouchTool.
It lets you make your own custom Touch Bar configurations for any app and much more.
I’ve been using it for 2 or 3 years now and can't imagine using my Mac without it now.
https://folivora.ai/

Cost is one off also free updates until version changes from 1.8 to presumably version 2 
Absolutely worth the money in fact all three Photo Designer and Publisher. Be aware from time to time there are offers and apps can be discounted.
 

On the overview pages for the different packages (https://affinity.serif.com/en-us/photo/full-feature-list/), i've used the Photo link as an example, it is indicated that the Touch Bar is supported. No details, though.