If you’re cutting the tops off the posts, they’re either too long or you’ve not dug your hole deep enough! You get a lot better finish by cutting the bottom off when you know how long it needs to be. I’ve never had to resort to supporting posts before the mix has set. If using post-mix, give it a splash of water and tamp down every 2-3″ or better still use some ballast and cement to make a 6-1 dryish/stiff mix. You should have at least 2 feet of post in the ground for a 6 foot fence, especially if you’re hanging a gate on one. Screws will be fine, just pilot the holes first and use large-headed screws. It’s not the most difficult job in the world, but like anything, making it look professional takes experience. Remember, measure twice/thrice, cut/dig once.