...if I buy steem does it fluctuate in my account as the value of steem changes?

Short answer: Yes, the estimated account value shown in your wallet uses the current market price of steem. So Steem you hold in your account has the same benefits of it increasing in price as would steem held elsewhere, such as an exchange like bittrex, poloniex, etc.

More technical answer: The estimated account value shown in your wallet isn't an up to the second valuation, but instead uses an average price over the last 3.5 days.

I also see it takes a few days for the conversion to take place - do I get the price that I see on the day of buying steem or a few days later when the conversion is completed.

When you use the 'convert to Steem' option in your wallet, it uses the 3.5 day price average as the exchange rate. Sometimes this can be beneficial, other times (like when the price has been going up for a few days) you can get a better rate by moving the SD's to an exchange to get an up to the second rate. (Remember though, there are fees charged on exchanges where the 'convert to steem' option has zero fees. Each exchange has their own fees, but for example on poloniex, the fees are 0.25% Takers and 0.15% for Makers as well as the 0.01 Steem fee when doing the withdrawal back to Steemit.)

The questions are great. I feel like I'm following what you're asking just fine. :)