
Other dogs, yes - he's at that age where he can be seen as an upstart so other dogs may grump at him more.
At home - this sounds like resource guarding, and it has nothing to do with dominance. You need to stop just taking things he's stolen and do two things: offer him something better as a swap, or (as long as it's not something dangerous he's taken) just ignore him and carry on doing what you were doing. Making a big deal out of it will only increase the value of what he's got (wow! they really want it back, it must be awesome! I'll try harder to keep it!). You can also throw treats in his direction as you walk past to make your proximity to stolen things a good thing. Also, practice swapping things when he isn't already guarding: swap something mediocre for something a little better, and practice until he's readily giving it up for the better thing, then increase the value of both and work up to the really good things, always making sure you have something better to give in trade. The more you practice, the more giving up what he's got will become both a habit, and no big deal to him.
On laps - a little trickier but the first thing I would do is get him checked out thoroughly. Dachsies are prone to back problems and although he's young, I'd still want to be sure he's in good health. How do you lift him? It might be that you're inadvertently hurting him or making him uncomfortable.
If that's fine, then teach him an 'off' cue so you don't have to move him manually (and it'll make being moved more pleasant for him) - very easy to teach. Encourage him on to a sofa or chair, then lure him off with something yummy and give the 'off' cue as you do it. Reward when he's moved, and repeat until he's doing it happily every time.
Neutering *may* help with the running off thing. *May*. It may not. I think you'd be best off upping your training to improve his recall, and keeping him on a long line or flex while you do that so he doesn't have a chance to practice running off and ignoring you. Neutering won't make any difference to the guarding at home, that is a training/handling issue.