The problem i have is with your choice of the word “should”. Should implies there’s a right way to do something. There is no right way to do photography. It’s an art. You’re free to do it any way you like. No one will say using Lightroom is the best or only way to edit photos.
Now do I recommend Lightroom? Yeah I do, and I’d recommend it to anyone getting started in photography. It’s a great tool that allows for lots of creative editing and produces high quality results. Most other editing software can do the same job.
Lightroom runs best on a full fledged computer. Can you use an iPad? Yeah but the mobile version of the app isn’t the same as on a PC/Mac. I’m not sure if there are any limitations or disadvantages since I don’t own an iPad.
It’s common…it means they’re shopping around and getting pricing from different photographers and they decided not to go with you. Nobody owes you anything until you’ve got an agreement/contract.