I'll try to answer your questions separately so I don't miss any:
have you tried it out on your store?
I have tried it and got sales during the test phase, so it does work, but like any other method it has it's advantages and drawbacks.
Does it trigger the website that an order has been made if it does not take the customer through the initial checkout process?
Unfortunately it does not as it goes directly through paypal and not shopify. That's the biggest problem with this method (for now) in my opinion
I'm not sure the orders will show up on his software or it's going to send an order confirmation email to my customer.
The orders will not show up on your agent's software and or on shopifies as previously stated. The paypal button is just embedded on the store and does not share any information with it (name, username, address, etc.). The way I found which works with this method is to copy your customers information from paypal (as it will show up there) and just make a draft order on shopify with the exact same information and mark it as paid. Then pay for the order and fill out the remaining information, i.e. shipping code and other notable information. This should start the email sequence you have set up. Although a little longer and less automated, it works.
We also can't give them the option of the discount code.
I've been trying to find the solution for this, as I've seen examples of paypal's buttons with input boxes where the customer could type in his/her discount code and then apply it to the final product price. This would take a little bit more code to do, as the smart buttons work with one "price", i.e they are set to one specific price and not to a changeable variable like your cart total price. I've exchanged ideas with people on here that had this problem regarding total product cart pricing with paypal buttons - basically paypal buttons only accept one price out of the box and you need to make a string variable with a "." separator so paypal knows what's up (I made the code and if anybody asks for it I'm willing to put it on here for everybody to see)
Do you know how to put the smartbutton on the product page and the last page of the checkout page where you put in your card information(not on the add to cart page as you have shown above)
The reason why I'm answering these questions is to give insight into the topic of what I currently know. The best way, in my opinion, of fixing this is to have api-s or webhooks which would connect the two platforms and make them exchange information when one or the other gets some. I'm currently looking into this and do not posses the knowledge to share completely so if anybody (who knows more) wants to share, feel free! Plus it would be a good idea to look further into this, as shopify feeds the facebook pixel with information which it uses for it's ads and if it does not receive information it could mess up the learning phase of the platform. Google ads could be another option, but I didn't look further into them.
If anybody has anything valuable to share on this topic, feel free!
Edit: Shopify seems to be deleting my posts regarding this everytime I post
Have you managed to get any progress on these buttons? I've been struggling for a while now not able to add them, and there seems to be no help online when it comes to integrating these buttons to Shopify.
I'd love to hear if you came up with any solutions! Thank you for your contribution so far, I appreciate it!