Question about Bitcoin

I know very little about the processes involved but have been surfing through wikipedia and related articles to try and understand how transactions are recorded in the blockchain. I know practically nothing about computer science so “For Dummies” answers would be appreciated.

  1. Is the “answer” to a proof-of-work “question” difficult to solve initially (cpu-intensive) but easy to verify afterwards? I can’t imagine how it could work otherwise if everyone on the network had to solve it first then agree.

  2. How does the order of transactions get verified within a block? If there is a lot of trading done within the 10 minutes that it takes to create a block, how is the official, more granular, time and sales record being verified? I could see that being a big problem in short term volatile trading.

  3. What’s to stop people from sending random transaction keys to the servers just for the sake of having their shenanigans recorded in the blockchain?

Let me rephrase question 3 and ask “Whats to stop the successful block miner from adding any kind of data to his block that he wants?”