[RPG] Can you craft a magic item that’s both a staff and a magic weapon

To quote the creation rules you cited:

To create magic items, spellcasters use special feats which allow them to invest time and money in an item's creation. At the end of this process, the spellcaster must make a single skill check (usually Spellcraft, but sometimes another skill) to finish the item. [...] It is possible for more than one character to cooperate in the creation of an item, with each participant providing one or more of the prerequisites.

The rules here clearly state that yes, the necromancer could fulfill the requirement needed for Necromancer's Athame if the necromancer had Craft Wondrous Item. What they are less clear on is exactly how this would work.

Helping someone work on a magic item would be an "Aid Another" action to influence the outcome of this final skill roll.

Here are the complete Aid Another rules:

You can help someone achieve success on a skill check by making the same kind of skill check in a cooperative effort. If you roll a 10 or higher on your check, the character you're helping gets a +2 bonus on his or her check. (You can't take 10 on a skill check to aid another.) In many cases, a character's help won't be beneficial, or only a limited number of characters can help at once.

In cases where the skill restricts who can achieve certain results, such as trying to open a lock using Disable Device, you can't aid another to grant a bonus to a task that your character couldn't achieve alone. The GM might impose further restrictions to aiding another on a case-by-case basis as well.

First, notice that you are required to make "the same kind of skill check in a cooperative effort." As a GM, I would rule that this means that all participants (the creator and the aiders) must work on the item 8 hours a day (or however long the creator is working) throughout its entirely. The aiders cannot simply show up at the end of the creation and aid for the final check.

Second, since a "cooperative effort" must be made, I would rule that the creator must expend as much effort as working unaided. This means that paralyzed characters cannot craft magic items, unless they themselves have some other way to work with the necessary tools.

Third, rules-as-written states "you can't aid another to grant a bonus to a task that your character couldn't achieve alone." This would mean that every character involved, be they creator or aider, must be technically able to craft the magic item themselves. However, note the following lines from the creation rules:

The DC to create a magic item increases by 5 for each prerequisite the caster does not meet. The only exception to this is the requisite item creation feat, which is mandatory.

Taking this into consideration, every character who can make a spellcraft roll and who has the requisite item creation feat can aid in the creation of a magic item. Each aider would fulfill any requirement they could, and add +2 to the creator's skill check if they succeeded in their roll.

For each prerequisite not met by the creator or any aider, increase the DC by 5, then roll the creator's skill check, adding to it for each successful aider.

To address your final question about the number of people working on a magic item, the rules for Aid Another leave this up to the GM. I would argue that the number of people lending aid is proportional to the complexity of the item. A scroll, ioun stone, or wand, for example, may not have any room for aiders; they would just get in the way. An Apparatus of the Crab, on the other hand, may have a dozen people working on its many parts.

Only [...] the various prerequisites required of the new ability to be added to the magic item restrict the type of additional powers one can place.

You are not creating a vorpal sword; the vorpal property is already on the sword. The relevant rule, quoted above, indicates that only the prerequisites of the new ability are relevant in this case. Thus you do not need to meet the prerequisites of the existing properties; you aren’t creating those, and the closest thing to saying you need them says:

Note that all items have prerequisites in their descriptions. These prerequisites must be met for the item to be created.

You aren’t creating a vorpal sword, so you don’t have to meet the prerequisites of vorpal. You are creating a new flaming property that happens to be placed on an already-vorpal sword.