Scd, it would help us if you include EXIF data. A hot shoe level is useful to have, but in order for it to help you, you also need a good tripod. Still, sometimes it is invaluable, your mountain photo doesn’t have a level horizon and while some forests have trees that generally grow vertically, the trees in your scene are leaning in different directions.
If the camera is not level, vertical lines converge. This is most noticeable if you are using a short lens. Most editors have a tool that can fix this if it is not too severe. You can also use a tilt-shift lens, but they are expensive and still have limitations.
I have a T2i. I find it most effective to use Av mode, most of the time. P and M are useful when using a flash and M is good for those times when lighting is unusual like back lit subjects or studio flash. The centre auto-focus point is almost the only one I ever use, although for some moving subjects and servo focus mode, it is helpful to turn them all on.
When shooting dogs, and children, it is better to get down to their level — assuming you can keep them from crawling all over you.
Weddings are expensive one-off events. Messing up a wedding shoot is painful for all concerned. Engagement shoots are a chance to meet the happy couple and see how well you get along on a shoot. Definitely do the engagement shoot. If they realize you are new to photography, they should also realize there are some risks, but also, if it is messed up, it’s not that big a deal, just wait for the next nice day and shoot another session. Either you will figure out how to shoot them or they will get tired of scheduling another session and get someone else to shoot them. Either way, you win.