(1) As far as hops and other sediment (trub) in the kettle, it is fine to pour it all into the fermenter if you want to. Some will say that some of the coagulated protein can provide nutrients for yeast. It will all settle out during fermentation, and there is no evidence that it contributes to off-flavors. That being said, it is hard to allow oneself to do that. I have personally struggled with balancing leaving behind trub and leaving behind too much beer.
(2) One technique is to whirlpool your wort during and/or after chilling by stirring vigorously in a circle. Do not splash or aerate the wort while it is over 170°F to avoid oxidation. The whirpool action will cause trub to form a cone in the center, and then you can gently siphon from the kettle to your fermenter from the edge, starting near the surface of the beer and moving the end of the siphon down.
(3) The recipe will account for some loss of wort in the kettle. In my experience with Northern Brewer and Midwest Supplies extract kits, that amount is about one quart.
(4) Adding water to the fermenter volume will not "water down" your recipe compared to the recipe's expectation. All of the sugars for the recipe are accounted for in the provided extract, and cannot evaporate in the boil. So your wort is very concentrated. When you top off to 5 gallons, you should hit the original gravity within a few points. So yes, always top off to the recipe's fermenter volume.
(5) In terms of topping off water, try to use sterile, de-chlorinated tap water, or standard bottled water (but not distilled water or reverse osmosis water). This also applies to all brewing water. Ask your municipality what they use for disinfecting water. If chlorine, you can boil and cool your water to remove chlorine and make mostly sterile. If chloramine, you can add campden tablets.