Yeah, don't expect too much...
Question #1 - For use, always store the glass electrode of a pH meter in water if you plan on using it. The glass takes time to hydrate and it's best to just keep the electrode in water if it will be used anytime soon. For long term storage, dry is fine.
For wet storage, do not store it in plain or even deionized water. Electrodes are typically stored in 3 Molar KCl or pH 7 buffer that has had KCl added to make it 3 M. Get a beaker (tall form (berzelius) beakers are good for this) and add extra storage solution in and place the electrode into it and cover the beaker with plastic wrap to slow evaporation. Or, if the electrode cap on the meter holds water, just pour some storage solution into it and cap it on the electrode. Store it upright as you don't want KCl to leak all over the place. The KCl will flow up the sides of the beaker as it dries, but remember - Do not fear the KCl Creep.
I'm assuming the electrode is gel-filled, i.e. there is no access hole to fill the inside of the glass electrode?
Question #2 - For calibration, I see you meter says it has 2 point calibration. What you need to do is determine what range you want to calibrate for. And by range, you can't just say, "I want to calibrate from pH 0 to 14, of course." pH meters don't work that way. You need to choose calibration points that are about 3 maybe 4 pH units apart. Common pH standards can be found for pH 2.5, 4, 5, 6, 7, 8, 10, and 12.5. For developer work, you probably want to use pH 7 and 10 or perhaps 10 and 12.5.
I suspect a meter like that may not work too well at pH 12.5, but who knows until you try. And with resolution of only 0.1 units, it will probably me fine, even at the ends of the pH range. It's the people (I often find them in labs) that seem to think if a pH meter reads to 3 decimal places, then it must be accurate... Good luck. It takes a lot of work to read pH accurately and precisely to 3 decimal places. Even with the best meters, 1 decimal place is usually easy, 2 is a much harder, and the 3rd decimal place is pretty much so unreliable and variable that it would make a fine random number generator.
Back to calibration - make/buy some solutions, place the meter in the first solution, adjust the meter, rinse the electrode with Deionized water and blot it gently with a tissue, and then place it in the next solution. Adjust the meter. Go back to the first solution and check and adjust if necessary, second standard and adjust if necessary. Repeat until you get it calibrated.
Then check you calibration frequently - like every 30 or 60 minutes. Just put it back into your standards and make sure it hasn't drifted since calibration. Don't go all day without checking the calibration.
To make solutions, you want to have buffered standards. Boric acid alone will not make a very good buffer - actually it will not make a buffer at all. Or you can mix them from a few stock chemicals - used in pairs to make the buffer solutions. I usually use ph 4, 7, and 10 for my pH work. They are typically made commercially using the following chemicals:
pH 4 - potassium acid phthalate (KHP)
pH 7 - Potassium Phosphate Monobasic and sodium hydroxide
pH 10 - boric acid and potassium hydroxide, or potassium borate, potassium carbonate, and potassium hydroxide
You can also buy dry powders instead of premade liquid standards. The powders come in little gel caplets or foil pouches that you empty into DI water and bring to a volume. Those are nice when you don't need a lot and use them infrequently.