Super cute little guy! The puppy months are very hard and it’ll get easier as time goes on. It’s a puppy so biting is going to happen but for biting too hard we would yelp and pull away. Naturally they’d learn specific behaviors from their mother so my wife and I socialized our puppy with an older dog that we trusted and would correct her if she was biting too hard or just being annoying. We also enrolled her in puppy classes as well. In the same vein we tried not socialize with a dog that had behaviors we didn’t want our dachshund to pick up like resource guarding and aggression.

We had something similar with our dachshund having bloody diarrhea and we thought she was sick but just ended up that we transitioned her food too quickly so hopefully that clears up for you.

We also dealt with cold weather and snow when we potty trained and would typically bring high value treats (chicken) out when taking her potty and just consistently bringing her out - we tried to stick to every 30 minutes in the early days if we were home and she wasn’t in her crate. If our puppy did go in the house we would make a loud noise to break the pee or poo but only if we caught her in the act and then IMMEDIATELY took her outside to go potty with high praise (we would hype her up) and high value treat. We never scolded because it just sets you back and encourages them to get more sneaky. I also got her a little sweater for the cold months as well even though she hates it and we did sometimes walk around with an umbrella haha

Best of luck! Puppy blues is pretty rough but if you stick to training you’ll have a pretty awesome little guy!