Shade shouldn't be a problem. In fact, a cover is good because it helps you control the sunlight and rain.

If the pile isn't heating up it's usually either bone dry or there's not enough volume. Aim for at least one cubic meter (or 3x3x3 feet).

If you have fresh grass clippings, add them - they will help a lot. A heap of grass clippings with nothing else will heat up on its own (but don't do it because it will smell).

Your cold compost is going to be fine, it will just take longer and won't cook the weed seeds. If you have more questions there's a composting subreddit: https://www.reddit.com/r/composting/