James...do NOT send your camera and lenses to Canon at this point in time. In my estimation, it's more about learning the exposure triangle and what affects what and how increasing or decreasing any of the settings affects the resultant picture.
In short, wider aperture = reduced Depth of Field - aka Plane of Focus - In the dog picture, your DOF is perhaps 2-3 inches.
Slower shutter speed = subject- and/or camera-motion caused blur. For handheld shots, I rarely shoot slower than 1/160th these days as my hands aren't as steady as they were 40+ years ago. For living/breathing/moving/waving/flying/crawling subjects, I sometimes get subject motion blur in 'posed' subjects at 1/60th. Anything slower than that you will very likely get some subject-motion blur...even the slightest twitch of an eyelid can't be stopped at 1/30th. Due to low lighting situations, I've been forced to shoot as slow as 1/10th and then toss out perhaps 20 or more to get ONE shot that does not have subject motion blur! I've been known to zoom in on the eye and hand when viewing the pictures on my computer to find the 'most sharp' of a series of shots of human subjects.
Higher ISO speeds = more noise, particularly in darker, somewhat underexposed areas. When I had my 60D and 24-105, ISO 2400 was where I typically stopped going any higher. But at times, I've 'pushed it' to 3200 and gotten acceptable results, with the noise mostly correctable in Lightroom. In my opinion, the 60D 'tops out' at ISO 3200 for usability. There are numerous threads in this forum about "I keep my ISO speed at 100 or 200 or <some ridiculously low value> and get poor results for indoor or nighttime shots". The low ISO speed is EXACTLY why they are getting poor results.
As someone on this forum mentioned perhaps 2 years ago already and I've "made it my own", getting the correct exposure is a 'compromise'. What are you willing to 'trade' to get '...'? I think of my 'compromising' with the exposure triangle is more of a battle than anything else. Give a little, get a little...etc. Many times I've pushed my 60D to ISO 3200 and STILL have to slow down the shutter to 1/30th or so to get good exposure per the meter in the viewfinder and histogram after the shot. But at that speed, I KNOW my keeper rate sinks very fast. And that was shooting wide-open at f4 on my 24-105.
In short, when I'm "maxed out" on two of the three exposure triangle settings, I have no choice but to 'make do' with whatever I have to do with the other setting.
Which brings me to another point... Very few lenses are at their sharpest at their widest aperture, or close to it. As you've indicated in this thread and an earlier one, shooting at f8, give or take, will produce sharper results. Yep! That's one of the 'compromises' that is not part of the exposure triangle, but is an important part of getting sharp results. Of course, shooting at f8 forces compensations in the other 2 triangle settings, which may cause less than 'the best' results, such as subject movement blur or ISO speed induced noise.
Lastly, as I was slow to learn until I had my 60D maybe 5-6 months, set your AF-mode to AI-Servo for ANYTHING that does or can move! No exceptions! My faulty thinking at the time was to use one-shot AF since I wasn't doing any multi-frame-per-second shooting. Dead wrong! AI-Servo, AI-Servo, AI-Servo. I can't tell you that enough!
And on the subject of AF (oops...one more, one more thing), limit the camera to only the cross-type AF points. That way you'll know you're getting the better focusing abilities of the camera. And, for what it's worth, I've learned to do most of my work using center AF point only. That way I ABSOLUTELY KNOW I am focused exactly where I want it focused, not where the camera thinks is a 'better' AF point.
Edit...yet another 'one more thing'...35 years ago when I banged my FD 35-70 f2.8-3.5 SSD lens against a door-jam as I was walking, I managed to knock something inside out of alignment. Living in Milwaukee at the time, it was a 90 minute drive to Canon just south of O'Hare airport. I got instantly 'looked at' by a service person and they concurred it needed to be repaired. Hopefully, Canon repair is still conveniently in the Chicagoland area.