I'm not sure what you're looking for, so I'm going to let you have the fool teardown:
Image 1: The composition is awkward, a bit too close to the paws on the bottom edge - it looks like it was shot just to have the branding in it. It reminds me of a classical side view portrait or ceramic bust, like the statues of great figures that stand on half height columns. Maybe if you comp'd it a bit lower on the body and more centered, it'd be cute... Caesar Canine or something like that.
The color temp seems a tad warm, but it doesn't bother me too much in this frame because of the wood background. The shadow at frame right / sub. left catches my eye, but not primarily (reading the frame from top to bottom, left to right) - at least not as much as the negative space. Some fill with a silver / white reflector (or foil/silver krylon on a white foamcore board) would help with that and add some detail to the darker tones of the pup's fur.
Also it seems to fall into focus at the bottom of the frame but out near the eyes / face, something to watch out for. Instead of bouncing from the side, try bouncing directly behind you (whichever direction the back of your head is facing), like a large direct softbox.
Image 2: This is where the color temp begins to bother me. Feels wayyy too warm and makes the BG look ...red-purple, falling to purple at the floor. Again comp, is a bit awkward and the collar is a tad distracting.
The shape of the light isn't too bad, but needs some fill on the opposite side (something difficult I can imagine with a canine), just to open up the shadows and add a catchlight to the other eye. I love the texture of the ears, so adorable! Shoot closer to f/8-11 to stop down the lens to really bring out detail there, back the sub. away from the background and then shoot with a long lens (this is where having a wrangler helps) to compress the image and hopefully give some blur to the BG (one advantage of the Kraft paper vs. seamless is price, but it is of thinner weight than seamless and shows wrinkles / dimples easier. I do use kraft for my tabletops, but things to consider in the future).
Image 3: I'm not a super big fan of the colors going on here. With the (too) warm skin tones and then the blue BG, its like the BG is fighting the subject for attention , it's too contrasting chromatically. The shade of blue almost reminds me of the background they use when you get your driver's license or an ID picture, you can vary the color (or at least the luminance) by varying how much light falls on it. As mentioned a tungsten lamp and flash are different color temps, you can either cool down the lamp or warm up the flash with a gel (or use your flash as the main light, and the tungsten as a warm hair light or background light, but when both fall on the same subject, it's a mess).
Lighting wise, I see a lot of vertical bounce (aiming flash vertically perpendicular to the subject). Something to think about is the old addage "what goes up must come down" - in this case, shadows. The areas under the chin, eye sockets, become unfortunately dark. Instead of bouncing up, try bouncing behind the camera. This relates to the idea that we discussed with the 1st image, having the light source become a large wall of light coming from behind you. This would create a large soft light source. In the image I see very small catch lights in the eyes and his teeth, which are rather distracting as they are the brightest points in the frame your eye goes to them pretty quickly.
Take a look at an edited version of your image that simulates what would happen with these changes: Black and white removes the distraction of color. A bit of fill from under to combat the directly upward/downward lights and shadows, minimizing the catchlights shows what would happen if moved away from a small source of light. The guy's posing is awkward, the collar intersects his adam's apple and it almost looks like you caught him by surprise. Shooting spouses can be awkward, just have him rellaaaaax. Not in a sit on the couch in your underwear with the game on kind of way, but dropping the shoulders, tilting the head a little, "think of how much you love me" kind of smile.
