1. Not completing full extension
Performing an exercise through the full range of motion will develop more muscle and strength compared to partial range movements. Muscles are meant to move through full range. Partial movements are sometimes used by bodybuilders when working a muscle to full fatigue. For most people, using full range of motion is the best option for increasing strength, muscle or body composition.
2. Arms forward of the chest
Placing your arms forward of your chest puts them in a biomechanically disadvantaged position. This makes it harder to do a proper pushup.
Fitness guru Jack LaLanne was able to perform a version of the pushup with his arms fully extended in front of him. Pushups with extended arm positions are advanced versions of the pushup and should be built up to over time.
Work with a personal trainer to learn proper form for the pushup and all strength training exercises.