Every digital camera I have seen so far has been designed for auto-focus. Auto-focus in most circumstances is much faster and more accurate than you are. Exceptions include macro photos, birds in the midst of tree branches, and brides behind veils. Manual focus is available for those times that auto-focus is frustrating you. Judge for yourself, I find most of the expensive lenses out perform the less expensive ones, but once in a while there are bargains. Sigma makes some great lenses which cost less than Canon’s, so possibly also less than Nikon’s. You have to do your research and see what works for you. Full frame bodies let you get closer to your subject with the same focal length, so you can get a shallower depth of field. This can be good or bad depending on what you are trying to do. Generally, the bigger sensors mean bigger photosites, so you get a bit more dynamic range and photos look better. Medium format takes all of that an extra step, at a couple of extra steps in price.
Post processing can make a photo better, or mess it up. Your assessment is pretty accurate. I’m fascinated by this one:
The blur on her arm is distracting and probably added in post. Yet, you didn’t fix the bride’s front teeth?
Flickr has changed, indeed. Asking it to show EXIF data results in a page saying it is private! Anyway, your challenge is to take photos with enough depth of field to show what you need to show with good detail and blur out background distractions, or to keep everything in focus if that is important to the photo. It is helpful to understand the effects of aperture combined with focal length, distance to subject and distance to background. Once in a while it may be necessary to add blur in post, but it is a lot of work to get good, realistic looking blur in post, so it is a last resort.
Studios are great, but limited. You can have total control over the light and subjects. At weddings you are lucky if you manage control over your subjects for the photo session between wedding and reception. Most of the rest covers a lot of ground and the best photos happen spontaneously so you have to be prepared and alert. Understanding your equipment, having it in your hands, configured as you need it, and being in the right place to take the photo at the critical instant is challenging.
You asked about posing. In this photo, for instance
two things really stand out for me. The burned out flowers and her left arm. The flowers stand out simply because they are burned out. Her arm stands out because it is the brightest part of the photo that is not burned out. There is not enough data in the JPEG to get the flowers back. Her arm could be darker by a stop and a half. Or, she could have put her left hand on his shoulder and he could have put his hand on her upper arm, covering most of her arm. The effect would work even better if he had his dark jacket on, instead of just a white shirt. Usually that hides some or most of her arm and acts to thin her a little. Adjusting how they stand to the camera, rotating them a little, sometimes helps to thin them out too. You have to do it on a case by case basis because each person is a different shape and what they are wearing can make a difference.
Try to get kisses just as they touch, but without duck lips, so faces are not distorted by pressure.