If you plan to regularly need phytoplankton I would use the bottle you purchased to start culturing your own. All you need are clear bottles/jars, an airline, fertilizer (there are special fertilizers you can buy for algae, but I’ve also just used miracle grow just fine as well), and light (sunlight works if you don’t want to buy one).
You just add some of your phyto to a bottle (empty 2 liter soda bottles are commonly used), add about 2X the volume of saltwater so it’s about 1/3 phytoplankton and 2/3 saltwater. Add a little bit of plant fertilizer (5ml or 1/2-1 tsp) is plenty. Put the airline in the bottle so the phyto doesn’t settle at the bottom.
Put under light.
In about a week or so, it should get a dark green. That’s when you harvest some for the tank and repeat the process to continue your culture. I’d recommend culturing at least 2 or 3 separate bottles as it’s common to have a culture crash.
If you only have a small amount gradually add more bottles as you culture the phyto.
as for your other questions, it should keep in the fridge for a month or so if you shake it up. You don’t need to add anything to the phyto. You should be able to smell if it goes bad.