Object flags and pie menus
To end the "in my way stompy feet" (I love when my sims do that, I'm always like "No! You shall not pass go and you shall not collect $200! You'll stay right where you are until your motives drop so low I take pity on you!!") - you need to add a line to the BHAV to allow person intersection.
I wasn't been clear enough, sorry about that. I don't want Sims to walk through it, although I'm sure I'll want to do that too at some point so I'm glad I now know how it's done. What I want with this object is for Sims to be able to use a OMSP placed above it. Right now it's saying the stove is in the way, and that it can't use the counter-OMSP that's placed there. I'm currently testing importing init and init common from a CC deco object I have that does allow OMSP above it, but even if that works I'd still like to know which flag it is that's causing that behavior I'm sure this won't be the last time I want to fix that.
EDIT: My attempt to fix it by using the init and init common of a CC deco object that did allow OMSPs did not work, so clearly there's more to it. That object does not have the allow person intersect-bhav, but perhaps I'm just missing the point and that would fix it?
I may know the answer to your TTAB problem (Nix will yell at me if do and don't remember!) - but I'll have to think on it. Having a head that feels like it's stuffed with cotton balls doesn't allow clear thinking, lol. So it takes some effort right now. (Stupid head cold!)
Or, as Klaartje said - clone a side table (not a dining table because of the eat slots), add slots and change the catalog placement. (Can be done in the OBJD, just change the category.)
OR - just clone a different object, like the fruit bowl - the TTAB is there (I use that as a base a lot). The thumbnail wouldn't show properly but that's easily fixed by deleting the entry in the thumbnailExtension in the CRES.
I haven't done anything with slots yet. I tried to follow a tutorial in the past, but it was too confusing and I decided to leave it for the future. I have since learned much more, so it may not be as confusing now, but as of right now I know nothing about how they work. Would the slot move when the mesh is changed? The surface of the stove is much higher up than an end table, so if the slot does not move it would end up being in the middle of the object. That's also half the reason I abandoned the idea of using a counter, because it's surface is a little lower than the stove and I knew the clipping would bother me. If it doesn't move, is that something that's easy to fix?
Meanwhile I'll try adding the bhav and see if that works. It would do as a temporary fix until I have the energy to re-do the entire thing with a different base object
To edit the position of a slot you'd need to know what height (at the very least) you want your slot to be. If you want to move it left/right or front/back, you'd need to know those too. Putting a mesh into MilkShape will help figure that out.
For the TTAB issue I'll try to clone the same object again, but check create stand alone object, and hopefully that includes a TTAB that I can export to my object like you said