Hi Anonymous,
Good questions! Finding good financial advice can be hard, especially if you have many people with different viewpoints providing different advice. The last person to comment is absolutely right about getting rid of your Target card, especially if you have the Target card with American Express, which was just rated worst prepaid card by Consumer Reports. And, store credit cards are HORRIBLE and will charge deferred interest once you pass the introductory time period. To answer your other questions...
1. I would leave this open, especially if your account is in good standing. Length of history makes up 15% of your FICO score. If you are interested in a card with reward options available, I would call a rep with Capital One and discuss switching over to a different card, such as the Capital One Quicksilver Cash Rewards Credit Card. It offers 1.5% cash back on all purchases since they don't have rotating categories, and pay no interest until August 2014, with a sign up bonus included. Here is a good post explaining how FICO breaks down your score,
http://comparewallet.com/what-determines-your-credit-score/
1A. If you choose not to try to get a better rewards card with Capital One, I would request a credit line increase, since you stated your concern with this card is that the limit is low, which doesn't help you much. If you are good with your account, which it appears you are, you may request a credit line increase on all accounts every 6-12 months. Leaving a card inactive will likely default any rewards you may have racked up and and leaving it inactive for 1-2 years, may cause them to automatically close your account. Make little purchases on it here and there, like gas or groceries. Closing your account will also alter your credit utilization ratio a bit, so I would keep it open.
1B. The drop in your score could be due to a number of things, such as credit inquiries, your balances, new credit lines opened, etc. You can find out for certain by checking your credit report (free from each credit bureau every year).
2. Rewards cards are worth it,
IF you use your card frequently enough to actually benefit from the rewards. One great travel rewards card that may interest you from Capital One is their VentureOne Rewards Card. As previously mentioned, speak with a rep to see if you can switch to a new card.
Hope this helps!