Would this work for a one year old for plane travel?

Sorry, I have no such experience; but, for one year old baby should be enough to use half of the pillow (one quarter to each ear). If you will use fresh pillow, then it will stick to ears of your child perfectly. Just cover ear canals - don't press the pillow into "pin" shape (there is no need, when you use fresh one). I'm sure that it will work. :) Oh, maybe it would be more convenient, if you use one pillow to each child ear (to make it more effective and easier to take out after the flight).

Are they white or transparent? I plan to use them at work, so I hope they will be invisible.

They are not completely transparent. But they are not completely white either. Earplugs will be less noticeable if you don't use 1 earplug per ear. This means that you need to split 1 earplug into 2 parts to get 2 less visible smaller earplugs. And you can get such small balls out of your ear by pressing your finger several times on the back of the ear. P.S. The case you see on the video is from another variation of these ear plugs - PQ Wax Ear Plugs 28

How can these be removed without pushing them further into the ear?

To remove the earplugs without pushing them further, simply press up behind your ear and they will fall out. We’ve shot a detailed video instruction for you (search in youtube: how to use pq earplugs) to see and learn exactly how to do it :) Victoria Your PQ Personal Assistant

Are they comfortable for sleeping?

They're very comfortable for sleeping from what our customers say :) These earplugs don't go directly into your ear canal, they only cover it. That's why they don't put pressure on your ears or feel bulky. You can sleep in any position you like and don't feel like you're even wearing earplugs at all! Victoria Your PQ Personal Assistant