I see you're in TX as am I. Gravel reflects a lot of light and heat so I don't really care for it especially around veg. I would go with cedar mulch over a weed fabric (you could also put cardboard under the fabric). If you have a slope problem, then try putting down a one by one piece of wood to keep the mulch from washing down hill. Just lay it on the ground... doesn't need to be nailed into the rock. I have the same problem by the way. I'm on the side of a rocky hill. I'm building raised beds, slowly but surely, in a pattern. I'll eventually have mulched pathways inbetween. Right now the weeds aren't a huge problem. I like the idea of mulch instead of rock because it will let natural rainfall slowly penetrate the ground. I'm currently using cedar mulch in all of my flower beds which are on gradual slopes and the mulch I bought 7 years ago is still holding up, not breaking down, or washing away.

There is not a minimum width, except what you plant needs for proper growth but there can be a maximum width. A 1 foot width may be adequate for vines, but how well the soil performs will depend on how well you prepare it. Adequate amounts of organic matter will help with moisture control and mulches will help with soil temperatures.

I spend a lot of time in the potager forum and this seems like a question tailor made for them! In my opinion, anything within about 3' of one another will benefit (or suffer) from the synergies of companion planting. Of course I have very little evidence of this, LOL, but in my experience that is the case. I like to stick nasturtiums in the corners of some raised beds so they spill out onto the gravel (which I use for paths in my veg garden).

What are you planning on growing? Some plants, like tomatoes, are very sensitive to juglone. Some others, like forsythia and daffodils, are not as sensitive. I grow everything in large containers (20+ gallons) because my small yard is surrounded by six black walnut trees. Twice in the past 10 years I accidentally included compost that had a small amount of walnut leaves and twigs in the mix for my tomato plants, and had plants completely collapse from walnut toxicity. Also, from what I have read from university studies, the toxicity from the living trees extends wider than the drip line, which can be 30-40 feet from the trunk. And it can take a year of composting to remove the juglone. From personal experience, I can't grow impatiens within 50 feet of a walnut tree, and I have seen other sensitive plants fail to thrive in that same range.