Buy a basic tuning kit an learn to correct those "zingers." The chances are your pin lock is bad and you have loose pins. You may be able to help a little by pounding them deeper into the pin block with a hammer - just watch the wound piano wire, you don't want to have that touching anything.
FYI, it is relatively easy to put bushings in the pin block. You have to carefully unwind the wire, keep it from falling off the the bottom pin, unwind the tuning pin, drive the bushing in and then put everything back together. You can see how to do this on youtube.
I suggest this because a piano like this will have zingers days if not hours after it's tuned. It could be so bad that you pull the tuning wrench to the desired tension and when you let go, the pin unwinds.
If it is that bad, and you don't want to attempt the bushings, if you have one string that holds tune, you can lower the remaining ones an octave where they will probably hold tune. It will not sound right, but there is nothing worse than a zinger.
You could also talk to you piano tuner abou putting some bushings in. ONLY do the zingers - don't let him sell you on a big expensive job.
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Regarding your play. Way too much pedal. In fact, learn to play it without pedal and that will force you to develop good legato.