[RPG] Can a lich be controlled by control undead

An item is allowed to have additional magics added to it, where the cost of the addition is the cost of the final product minus its current value. That is, take a +1 quarterstaff (2300 gp) and make it a +2 quarterstaff (8300 gp) for 6000 gp. See Creating Magic Items – Adding New Abilities:

Adding New Abilities

A creator can add new magical abilities to a magic item with no restrictions. The cost to do this is the same as if the item was not magical. Thus, a +1 longsword can be made into a +2 vorpal longsword, with the cost to create it being equal to that of a +2 vorpal sword minus the cost of a +1 sword.

If the item is one that occupies a specific place on a character’s body the cost of adding any additional ability to that item increases by 50%. For example, if a character adds the power to confer invisibility to her ring of protection +2, the cost of adding this ability is the same as for creating a ring of invisibility multiplied by 1.5.

For many items, combining functions (rather than upgrading them as with weapons) in one item carries a price premium equal in value to half the value of any functions after the first. This would also be part of the cost of adding magic to an already-magic item.

Stuff like directly using hides or medusa heads to make items, kind of. By default, yes, your character needs to have the appropriate materials (whose worth equals the crafting cost of the item), but what the “appropriate materials” are is left undefined and up to the DM.

Thus a DM may decide that a spike, gem, etc. is worth a certain amount towards the crafting cost of the item (e.g. that sword costs 2000 gp to make, but the gem you just found can be used for a part of it: you only need to provide materials [steel, leather, whatever] worth 1000 for the remainder of the sword). Most of the time, though, it’s more like “I go to the blacksmith and buy whatever I need for the sword from him.” Requiring specific, especially rare, materials doesn’t really occur in the rules except sometimes for certain spells (e.g. raise dead requires diamond dust).

I haven’t personally seen one, but I’d be surprised if no one’s drawn up lists of explicit materials for particular items. I doubt it’s official, though.

A destroyed creature with the template class lich refoms up to a few miles from its phylactery

The Wizards of the Coast Savage Progressions Web column "Lich and Weretiger Template Classes" includes in its description of the lich template class's class feature phylactery the following text:

Once the phylactery has been completed, the lich can avoid permanent destruction as long as her phylactery survives. If she dies or is destroyed, she reappears 1d10 days after her old body's death. She gains her new physical form by grafting her undead spirit to a humanoid corpse, mindless undead, or some weak-minded creature within a few miles of her phylactery. The new body has all the abilities and powers of her old one, though any items she used to carry are lost (probably taken by those who slew her old body). Likewise, any spells or effects bound to her old body with permanency do not spontaneously appear on her new one. Most liches who recover from death spend a year or more tracking down their items and learning more about their attackers, and it is not unusual for a lich to wait decades before exacting her revenge.

Emphasis mine. Whether the same is true of all basic liches is unknown, but without additional guidance this seems a good enough rule as any.