Hello fitbabe,
Welcome to the forum. Here are answers to your questions.
1. Yes. You can buy tickets at the lottery headquarters and district offices.
2. I have not noticed any real difference in buying tickets from the vending machine vs the counter. Go for whichever has a shorter line. The only noticeable difference is that the tickets in the machine are filled faster because of greater foot traffic. That usually means that the book/roll number is higher for the vending machine rather than behind the counter.
3. For the $2 I like the $1,000/week for life. Seems overdue. Ditto for the $5 - $2,500/week for life. None of the $10 tickets excite me right now. The last top prize in the $10 Monopoly game was claimed. The $5,000/week for life may still be premature for a top prize. I don't play the crossword games but they may be a reasonable pick for a $10 game. For $20 - the old $20 Gold Rush, the new $10k a week for life is probably due for a top prize in the next few weeks. But that game is fairly punishing for higher tier prizes.
4. The number in parenthesis next to the bar code is the ticket number in the book. The book number is the second set of numbers. For example, for the $20 gold rush - 1249-2051000-5-12 (18) - the 1249 is the game number, the 2051000 is the book number. The 5 is a random security number. The 12 corresponds the the ticket number on the bottom of the front side of the ticket. The 18 is how many tickets are left in the roll.
I wish you the best luck!