To practice at night, I used the practice pedal to mute the piano. Does practicing the piano with the mute pedal damage the piano in the long run? Would it affect the hammer or the string in a negative way? If it matters, the instrument is a Yamaha upright.
For the mechanisms I'm aware of for quieting a pedal, no, there is no risk of damage to the hammer or strings and no reason in general to not hold the pedal down.
With a true una corda pedal, the entire action of the piano is moved slightly to one side, so the hammers don't strike all the strings or they strike the single strings a more glancing blow. The actual movement of the action causes a slight amount of wear on the piano, so quickly pressing and releasing a true una corda pedal over and over again could prematurely wear down that mechanism. Merely holding the pedal down for long periods is not an issue at all, aside from eventual uneven hammer wear. But after that much playing, your hammers will be worn anyway, evenly or unevenly, and you would want to recondition or replace them. And we're talking years (after the break-in period).
For pedals that drop felt in between the hammers and strings, that is definitely not an issue. In fact, the pianos I've played that do this have had a pedal lock where you can leave the felt in place indefinitely without holding your foot down. I suppose eventually the layer of felt will get compressed and its damping ability will be reduced, and you might want/need to replace that felt.
In general, pianos suffer a bit from environment changes and regular wearing down of moving parts. You should have a piano tuned and checked (and repaired if necessary) at least twice a year - especially if you live in a temperate zone where you have a real summer and winter. You'll need to have maintenance done for certain over the life of the piano, but using one of these kinds of pedals won't cause unusual damage or wear that would require more frequent than usual maintenance.
On the assumption that your piano has three pedals, and the middle one is not a sostenuto pedal, then it's a practice pedal, which can be slid to one side to lock it on.
Doing this usually moves a curtain of felt down so that it is placed between the hammers and the strings. A very different action to the una corda (soft) pedal on the left.
There will be no wear or untoward happenings to your piano while this is deployed - the very fact that it can be locked is a big clue. The main point of it is that it lessens the dynamics of your playing, without you having to adjust how you strike the keys. You could even, at a push, use the soft pedal as well, but that will change how you need to play, due to the fact on the majority of pianos, it moves the whole lot of hammers closer to the strings, so they can't be made to hit as hard.
Incidentally, Mine's a Yamaha harp in a different case, with practice pedal. My nearest neighbour is over half a mile away, so the middle pedal doesn't get a lot of use! I'm into the fourth year since the piano was tuned (only tweaked) after a big move, and there's no sign of it needing a tune just yet.
Actual answer - no, it won't hurt the hammers, strings, or felt. Although it's going to be worth checking the felt curtain after about twenty years! It's still a good idea to play it normally, when possible, if only to appreciate how good it can sound!