“How can I change the text size on the labels”

Actually, users cannot change text size!  This is confusing to many users, but there is a reason for this.

The app tries to make the best use of the available space. Of course, the amount of text to be printed in each label can be very variable as the names and addresses can have different lengths. Some addresses might use 3 lines, others 6, for example. Some address lines can be very long, others very short.

Therefore, the app has to change the size of the text, on a label-by-label basis, to fit the name and address in that label. The result is that the sheet looks like the names and addresses are all over the place, and with different text sizes. However, if you peeled the labels off, the text for that label should hopefully look correct.

Having said that, you are able to limit the size of the text, via the settings. This is aimed mainly at large labels. If the text size isn’t limited, as before, the name and address would be made large, to fit the label. This can result in very large text, which might not be as desired. Therefore, the user can go to setting and set a maximum size. 

Can I transfer my lists to another device e.g. from iPhone to iPad?

You can copy your lists to another device. If your lists contain names from your Contacts, then the Contacts in the two devices should be the same i.e. you should sync the Contacts via iCloud or iTunes.

To transfer AddressLabels lists to another device, you need to do a backup to dropbox on one device, and then a restore from dropbox, in the other device. This is done within the app itself. For more information, read https://addresslabels.app/ios-mac-list-transfers