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With regard to Items Broken By Sunder: Your GM was wrong. However, if the Item was destroyed, then he was right.
Sunder
You can attempt to sunder an item held or worn by your opponent as part of an attack action in place of a melee attack. If you do not have the Improved Sunder feat, or a similar ability, attempting to sunder an item provokes an attack of opportunity from the target of your maneuver.If your attack is successful, you deal damage to the item normally. Damage that exceeds the object's Hardness is subtracted from its hit points. If an object has equal to or less than half its total hit points remaining, it gains the broken condition (see Conditions). If the damage you deal would reduce the object to less than 0 hit points, you can choose to destroy it. If you do not choose to destroy it, the object is left with only 1 hit point and the broken condition.
Broken: Items that have taken damage in excess of half their total hit points gain the broken condition, meaning they are less effective at their designated task. The broken condition has the following effects, depending upon the item.
If the item is a weapon, any attacks made with the item suffer a –2 penalty on attack and damage rolls. Such weapons only score a critical hit on a natural 20 and only deal ×2 damage on a confirmed critical hit.
If the item is a suit of armor or a shield, the bonus it grants to AC is halved, rounding down. Broken armor doubles its armor check penalty on skills.
If the item is a tool needed for a skill, any skill check made with the item takes a –2 penalty.
If the item is a wand or staff, it uses up twice as many charges when used.
If the item does not fit into any of these categories, the broken condition has no effect on its use. Items with the broken condition, regardless of type, are worth 75% of their normal value. If the item is magical, it can only be repaired with a mending or make whole spell cast by a character with a caster level equal to or higher than the item's. Items lose the broken condition if the spell restores the object to half its original hit points or higher. Non-magical items can be repaired in a similar fashion, or through the Craft skill used to create it. Generally speaking, this requires a DC 20 Craft check and 1 hour of work per point of damage to be repaired. Most craftsmen charge one-tenth the item's total cost to repair such damage (more if the item is badly damaged or ruined).
Damaging Magic Items
A magic item doesn't need to make a saving throw unless it is unattended, it is specifically targeted by the effect, or its wielder rolls a natural 1 on his save. Magic items should always get a saving throw against spells that might deal damage to them—even against attacks from which a nonmagical item would normally get no chance to save. Magic items use the same saving throw bonus for all saves, no matter what the type (Fortitude, Reflex, or Will). A magic item's saving throw bonus equals 2 + 1/2 its caster level (rounded down). The only exceptions to this are intelligent magic items, which make Will saves based on their own Wisdom scores.Magic items, unless otherwise noted, take damage as nonmagical items of the same sort. A damaged magic item continues to function, but if it is destroyed, all its magical power is lost. Magic items that take damage in excess of half their total hit points, but not more than their total hit points, gain the broken condition, and might not function properly.
With regard to upgrading magic items your GM was definitely wrong:
Adding New Abilities
Sometimes, lack of funds or time make it impossible for a magic item crafter to create the desired item from scratch. Fortunately, it is possible to enhance or build upon an existing magic item. Only time, gold, and the various prerequisites required of the new ability to be added to the magic item restrict the type of additional powers one can place.The cost to add additional abilities to an item is the same as if the item was not magical, less the value of the original item. 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 longsword.
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.
That said, It's his table.
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1. Can you fix a destroyed magic item - YES. See the Make Whole spell. Also, I think the magic items crafting rules have something about repairing magic items.
Make Whole (partial quote): "Make whole can fix destroyed magic items (at 0 hit points or less), and restores the magic properties of the item if your caster level is at least twice that of the item. Items with charges (such as wands) and single-use items (such as potions and scrolls) cannot be repaired in this way."
PRD Sez: "Repairing a magic item requires material components equal to half the cost to create the item, and requires half the time. The make whole spell can also repair a damaged (or even a destroyed) magic items—if the caster is high enough level."
2. Can you enchant an existing magic item to add more powers - YES for weapons and armor. Other magic items with progressions also allow for improvement (such as improving a Cloak of Resistance +1 to +2, then +3, etc.)
PRD Sez: "Fortunately, it is possible to enhance or build upon an existing magic item. Only time, gold, and the various prerequisites required of the new ability to be added to the magic item restrict the type of additional powers one can place."
Hope this helps!
Make Whole can repair destroyed magic items:
Repairing Magic Items
Repairing a magic item requires material components equal to half the cost to create the item, and requires half the time. The make whole spell can also repair a damaged (or even a destroyed) magic items—if the caster is high enough level.
Recommended interpretation for GMs
Enhancing existing magical items:
Player A wants to add a 20,000g enchant and a 1,000g enchant to an item.
According to RAW, they can do the 20,000g first and the 1,000g second - making the item cost 21,500g. However, 1,000g +1.5k20,000g = 31,000g if the order was reversed. The order of adding enchants to an item should not matter. I advise every GM to multiply the most expensive item by the highest multiplyer when figuring out costs, not the newest addition to the item.
Recommended interpretation for GMs
Enhancing existing magical items:Player A wants to add a 20,000g enchant and a 1,000g enchant to an item.
According to RAW, they can do the 20,000g first and the 1,000g second - making the item cost 21,500g. However, 1,000g +1.5k20,000g = 31,000g if the order was reversed. The order of adding enchants to an item should not matter. I advise every GM to multiply the most expensive item by the highest multiplyer when figuring out costs, not the newest addition to the item.
Weapons and armor don't multiply by 1.5 to add enhancements. You only do that if you combine items together.
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Combine items? Never heard of such a thing
Personally, I wouldn't allow it unless you're an experienced GM. If you're new to GMing, or don't understand the item creation rules, then you should just limit players to the standard items found in Pathfinder (i.e. no custom items). Note that enchanting a sword to +1, then +2, then +2 Holy, then +3 Holy Keen, etc., is still considered a standard item. But taking a cloak of resistance +3 and adding +2 STR is a custom item. Custom items are optional and many GMs don't allow them (but many do).
If you feel you can handle it, then allow it, but be sure to keep on top of what is being created and exercise your judgment as GM if you feel something doesn't fit the setting, doesn't fit the item or otherwise seems wonky to you.
Recommended interpretation for GMs
Enhancing existing magical items:Player A wants to add a 20,000g enchant and a 1,000g enchant to an item.
According to RAW, they can do the 20,000g first and the 1,000g second - making the item cost 21,500g. However, 1,000g +1.5k20,000g = 31,000g if the order was reversed. The order of adding enchants to an item should not matter. I advise every GM to multiply the most expensive item by the highest multiplyer when figuring out costs, not the newest addition to the item.
"Multiple different abilities. Multiply lower item cost by 1.5". It's on Table: Estimating Magic Item Gold Piece Values under Special.
So your proposed houserule is based on a false assumption and ends up the precise opposite of RAW.