Yes, there is usually a tab, either on the metal terminal or inside the shell. I do enough of these to justifying buying the special tools for 'releasing' the locking tabs. In many cases, you can use a small flat-blade screwdriver but you need to be careful. (That's what I used before I bought the tools.)
(Most of the tools I have are for working with weatherpak connectors or similar, which really require those tools.)
Yes, two shells ideally ... I was thinking of a picture I saw online. with a single one-way shell. From what I saw in the picture, I assume someone broke the other shell. (It actually had two bare, un-insulated spade terminals at one end ... Yikes!)
Yes, I usually replace the old wires with new. But that's because I'm often strapping a whole new harness, or at least a section/bundle.
If it's just a single connector, it's a judgement call. What's the condition of the old wire? What's at the other end of the wire? How much slack do I have? Can I make a neat, professional-looking splice? Et cetera, ad nauseam.
(I can usually refurbish those with hard plastic shells ... the molded rubber-like connectors are a PITA and usually have to be replaced with a complete new pigtail.)
I do NOT like using the inexpensive, readily available zip-ties on wiring ... they tend to eventually cause issues with the wire insulation. (There are zip-ties made specifically for wiring, which tend to be wider and use better plastic ... but those are hard to find and more expensive.) In the past, I've used vinyl electrician's tape, wrapped around the bundle at 6-8 inch intervals. Now I use the self-adhering silicone tape.
Repairing the plastic shells themselves is often difficult, frustrating, and impossible. (Gluing plastic is an art, bordering on wizardry.) It's possible to buy new plastic shells for the more common types of connectors but it requires quite a bit of 'internet digging' to find a source. The connectors for dual ballast resistors are somewhat unique so would require a lot of searching, if they're available at all.
