Try to check what is your HU model, is it with 2 RCA pre-out or 1? If got more than 1 then you no need pre-amp or e-crossover anymore(1 of the cause of airplane sound)
You cannot use your 4 channel amp with 1 channel for your sub and 3 channels for your speakers. You have to use 2 channel to bridge it and balnce 2 for speakers.
4" components is no good for bass, is more on voice only, but is good for you if you don't want to cut a hole to put 6.5" on your door assuming your door have no speakers. Then you can put a 6.5" component at rear. But alot of people say 6.5" must put on door only the effect will be good. But bear in mind local car door cannot stand heavy bass, you might end up some screws lossen and creating sounds on your door.
For your budget of 1k, you cannot get everything you want. The most is you can only get an amp for sub a 12" sub and box.
Is Alpine Replica V12 - amp you are refering that selling on ZTH or Lelong one? If yes then it can only use for components and not sub. I have one and thinking of letting it go.