Hello Zisi Wolf,
Natalie Smith gave a great answer and I am just going to try to add another 2 cents to it. So, yes, start off with some form of assisted push up, wall push up, then push up off a bench (hands on the bench), notice the elbow angle in that it is near parallel to the chest.
Also, as per the plank, maybe they are doing the plank wrong? There are numerous ways to cheat on planks. tell them to dig there forearms and hands into the mat and pull back towards their belly while squeezing the glutes. That they cant cheat.