It depends on your customers. I personally definitely prefer paper, but I see why others wouldn’t.
The pros of paper are that it is well known and well understood, and there can not go much wrong with it. People know how to fill out forms. The culprits are also well known and well understood. You need to enter the data manually, and you can have problems reading it etc.
When using electronic devices, you need to make sure they actually work. Tech trouble happens more often then you think. You need to have tech support available when the connection to the server has trouble, or when the app crashes, or whatever. Especially when the amount of devices is small and you need every of them (if you have 50+ devices and one doesn’t respond anymore, you simply take it out of circulation until it can be fixed, if you only have 5 or so then not having one will be a significant setback).
Then you will need to have people that can assist the customers with the electronic form. Especially elderly people (or in general, not tech-savvy users) might be very uncomfortable with it.
So in the end it boils down to what costs less, the overhead of having to enter the data from paper forms into your system or the overhead of having tech support available and having people available that can assists with entering the data. That is hard to see from the outside.
You can always do the hybrid approach. Have some tablets available and encourage users to use the tablets, but also keep some paper forms on hand. You can use paper forms for people who don’t want the tablet (e.g. elderly people) and also have them available in case the electronic system breaks down. This also lets you get your own experiences with the system and how well it works with your customers and allows you to gradually phase-out paper if that turns out to be beneficial.
Whatever the user inputs is already entered into the system. Highly legible.
No. You should never design a system in that way. The filled out forms should be submitted into a separate system, where they can be audited (e.g. for inappropriate, offensive or otherwise malicious inputs) and then electronically be transferred into your database. This also allows for corrections or for only partial data transfers, depending on how its implemented. I would never have users fill out forms that directly change my data set (never trust user input)!
Another thing you can consider is letting users use their own devices. Prepare it as a web form. You can have a validation token in form of a QR-code. Hand the customer a small paper card with the QR code. They scan it, open the web site, fill out the form, and the token gets invalidated and can not be used again. This way, you do not have the bottleneck of bringing lots of your own devices. You should still have some devices that you can lend people who don’t have a smartphone, but you can avoid the bottleneck of only having a few devices.