First, the obligatory statement that this is kinda off-topic for philosophy and would probably get more and better results in another, more appropriate section.
And second, a disclaimer that although economics is a side interest of mine, it's been more than a decade since I've had any formal schooling in it.
1. False, I think. "Highest possible price" seems like a vague term, because the highest possible price is dependent on the number of sellers in the market. Monopoly pricing is not necessarily the highest possible in any circumstance, though I think it is always higher than market pricing. Monopolies can realize some economies of scale though if they're large.
2. Uncertain. There is a _correlation_ between "bigness" and being a monopoly, but not necessarily causation. If you run a ma-and-pa drugstore in a small town and you're the only drugstore in town, then technically you are a local monopoly.
3. False. Simultaneous price increases can also result when the cost of raw materials rises. For instance, if the price of oil spikes from $75 to $100 a barrel, all gas stations will raise their prices, not because they are colluding but because the cost of their raw material has gone up.
4. Marginal costs & revenues are the costs and revenues on each _additional_ unit produced, not on _all_ units being produced. This is where the age of my memories may be hindering my answer (i.e. I could be wrong), but I think you could still have _total_ costs and revenues being unequal.
Hope this helps (or at least doesn't hurt)!