PayPal Checkout Button

Hello,

The fact that the paypal button isn't be displayed exactly in the same place as the other payment methods and voluntary because the process is totally different compared to other payment methods.
Now, you have this code in the paypalexpress.php file :

Hi,

The goal of the PayPal express checkout payment method is to skip your checkout. When you click on the button, you get redirected to PayPal's checkout screen, pay for your purchase, and only then is the order created and confirmed.
That's also why it doesn't appear with the other payment methods since its goal is precisely to skip your checkout.
Similarly, having to pay an already created order with PayPal express checkout should not happen as the orders made with it will be already paid and the others shouldn't have the payment method listed on that payment page.
The fact that it doesn't display the name of the payment method but its folder name is because the payment method selected for the order is not among the ones loaded as valid payment methods, but since it was set before in the order is still displays it in the dropdown as to not change the selected payment method for the order. But because of that it doesn't have access to the name.
But again, that situation should normally not happen. I suppose you must have either created the order in the backend or changed the payment method of an order to this one to get it listed there.
However, reading your first message, it seems that you want to use PayPal as a normal payment method, where the customer goes through your checkout and can select it among all the available payment methods. In that case, you probably don't want to use PayPal Express Checkout but another PayPal plugin like PayPal standard, or PayPal Advanced.