You have a lot of good questions there, opus64.
That's a good thing!
I'm no expert but if all or most of your piano experience in the past has been digital pianos, you are in for some surprises, some pleasant and some not so pleasant in regards to acoustic pianos.
First off, a concert tuning is basically a very high quality tuning usually done by a concert piano technician. A concert piano tech is basically a piano technician with a great deal of experience and technical skill. They can tune and regulate a piano (concert piano or other) to a very high level.
Also, in regards to pianos going out of tune, it begins (going out of tune) immediately after being tuned. A high-quality acoustic piano can be tuned well by a good tuner and some of the unisons (multi-string notes) will start to get twangy very soon afterward, especially if played hard. A really good piano tech (concert tech) can achieve a higher level of tuning stability than a less experienced tuner or a tuner who doesn't take the extra time and effort to achieve the good tuning stability.
Even so, concert pianos at music halls and concert venues are tuned often, usually daily at least and sometimes multiple times a day after each pianist performance. Same with recording studios... the pianos are tuned frequently, usually before each recording session.
So, it is somewhat normal to expect that some notes will sound a bit out of tune if your piano is play hard and often.
And, yes, you can find a concert piano technician to tune, regulate and voice your piano, but keep in mind they usually charge more than the average tuner; but are usually worth the difference.
Hope this helps, at least to some extent.
Happy piano playing!