'I can't get a solid
piece in the length that I cut because it starts breaking apart.'
Place the Ink blocking on a firm surface face down (paper backing side up) and cut with a sharp knife into strips.
They should be at least 2mm thick - this might stop it breaking up on you.
If the pieces are too thin I find that the ink just goes through it anyway, so you have just wasted materials and time - it's not that expensive.
To apply, peel one end and attach it to the inside of your thumb, then when you continue to peel the rest off you are holding it with the tips of your finger.
Then when you start to apply, the bit stuck on your thumb won't get caught on the screen or tangled up on itself.
It's not easy but try to touch it as little as possible.