Most companies pick one shirt color but some companies feel their employees will be more comfortable if they are allowed to pick their own shirt colors. If you have employees pick their own colors make sure your logo colors are readable against the different shirt colors or request different thread colors depending on the shirt color.
Possibly. There are many factors involved including the size of your original design and the type of detail it contains. The primary consideration for cap designs is they are limited to 2" high. If your left chest design is horizontally orientated then its very likely it will work for caps without changing the artwork although it may need to be set-up so it runs (embroiders) from center out which differs from most left chest designs.
What if your left chest design is higher than 2"? You can either eliminate some of the detail, rearrange the design elements so they have a horizontal orientation or consider using just your business name. For a attention-getting look consider using your business name and one element of your design and have your logo centered on one of the front panels rather than locating in the center front.
Docx files are word processing files rather than artwork files so they aren't as good at handling images, fonts and colors. Because of this unexpected things can happen like substituted fonts when docx files are opened on a different computer system. To avoid these problems its best to not use docx files.
Advertise your business during the colder months by having your employees wear embroidered jackets, sweatshirts and polar fleece.