Connected in the sense that one can be used as a political cover for the other, sure. But nuclear fuel and nuclear weapons require very different enrichment regimens. Nuclear fuel usually requires 20-30% enriched uranium. By comparison nuclear weapons require plutonium, enriched to near 100%.
The cover is not only political. One needs the plutonium for enrichment in the first place. If you fuel a nuclear power plant with uranium-235, you get it is a by-product.
I consider nuclear proliferation as one of the largest dangers we are facing, because it increases the risk of conflicts escalating into nuclear wars. So everything that makes it harder to create nuclear weapons is important.
The civil nukes have all been massively subsidized by military usage. There is no way a purely civil program could have shouldered those costs. And even the civil program is, separately, massively subsidized. Again, no civil plant could afford to operate without.
Incorrect. Plenty of nuclear programs did not receive subsidies from military usage. South Korea, Japan, Sweden, and Belgium for instance all have significant nuclear power development but no nuclear weapon programs.
