First you don't NEED to take daily readings....Just wait til it's been 7 days, and take a reading...then on the 10th day, take another...if the readings are the same, then you can rack...
Or you can do what many people do if they do rack..and that is wait 14 days, then move it to secondary
But you will find that many of us do not secondary at all, instead we opt for a month long primary, then bottle...we only secondary if we are dryhopping, adding fruit, or oak...otherwise we let the yeasties do what they do best and clean up thier house...
Either way don't be so quick to move your beer, leaving it a little while on the yeast, allows them to clean up the byproducts of fermentation, which will result in fewer off flavors...
But as to your other question, storing it in a sealed container, with distilled water, the starsan can last several months. That's why many of us fill a spray bottle with starsan/distilled water for those spot sanitizing needs, like sanitizing our turkey baster or wine theif and the bucket lid when taking a grav reading.
I put a lot of tips for using sanitzers like starsan and iodophor in this thread
https://www.homebrewtalk.com/f39/sanitizer-question-54932/?highlight=sanitizer+question
But like I said, you really don't need to hover over your beer, taking daily readings...doing that could actually introduce and infection.....just wait at least a week then take the first one....
John Palmer, in How to Brew even advocates not rushing the beer out of primary.
Leaving an ale beer in the primary fermentor for a total of 2-3 weeks (instead of just the one week most kits recommend), will provide time for the conditioning reactions and improve the beer. This extra time will also let more sediment settle out before bottling, resulting in a clearer beer and easier pouring. And, three weeks in the primary fermentor is usually not enough time for off-flavors to occur.
(and)
....As a final note on this subject, I should mention that by brewing with healthy yeast in a well-prepared wort, many experienced brewers, myself included, have been able to leave a beer in the primary fermenter for several months without any evidence of autolysis.