So we've been able to tune the horribly out of tune F2# string, on my inexpensive Riga piano, with this improvised piano tuning "hammer":

Well not perfectly, but it's a major improvement.
But I have another problem, the B6 key's mechanism is making a ticking sound when it's depressed, take a look on youtube

Do you have any suggestions for a quick fix ? Do you need any more angles? I've taken out the mechanism to have a look, but wasn't able to identify anything, because I didn't know what I was looking for...

You are likely to ruin tuning pins with an improvised tool like that. Have you ever heard the expression, "Penny wise and pound foolish"?

I can't see from the video, but it sounds like the hammer butt felt is missing. When the jack goes back to its rest position, it is hitting bare wood, causing the "tick". You'll need a bright light to look behind the jack, to see if this is actually what is happening. The piece of felt is rather small. If it has come unglued, it may stuck somewhere near where it fell out.

When trouble shooting noises, try to isolate parts.

Trip the jack and let it go. If you hear the click, it is indeed a missing butt felt.

Just cut a small square of felt, similar to the other ones, and add a drop of glue and use some long tweezers to grab the corner of the felt. Trip the jack and hold it while you position the felt square at the back, behind the jack, and onto the butt, NOT onto the butt buckskin, just onto the wood area at the back where the lost piece was glued.

Spend a lot of time looking at the parts moving before you try this. Be sure you understand what I am saying and why before you try this. Not because you will break something and it will be unrepairable (Yes, you can replace a worn tuning pin, although you'll probably wear out your homemade hammer before that happens) but because I want you to be able to have success with this, or any repair you try, with the least amount of aggrivation possible.

It has been said, when asked a question, or asked to perform a skill, one difference between experts and amateurs is that the amateur will begin right away, while the expert begins after a good period of reflection.

Good luck.

So basically when the tuner came in last Sunday to tune the piano, he removed the action to clean the inside of the piano and he said, that if I ever will be looking for a new piano and it will make the ticking sound after a key is released, most likely it's because that part of felt is missing due to moth damage. Then when he was tuning it, he noticed the ticking and said "I don't understand, the felt part doesn't seem to be missing", then he did something (I believe with a screw driver) that stopped the ticking, but later it came back...

As always it can be many things including a piece of glue in the way. Sounds like you need a new tech....to eliminate your..tick.

On a Riga, (but even on a Renner action), it can happen that the (red) cushion fall , and the jack ticks on return . but this can be seen with a flash light, and that jack is not at the same rest position than its neighbors.
if you move the jack only with a small screwdriver you will hear immediately if it is in fault.

A customer of mine had that problem and glued back the little cushion without dismounting anything. A simple drop of white glue, preferently only at the bottom back side of the cushion, and once reinstalled the jack will hold it in place for the glue to set.

A drop of glue on the old cushion could make that noise , if it is not the missing cushion check the key return, check the hammer shank return, test with the sustain pedal engaged (dampers inactive)

An horribly out of tune string mean that the tuning pin is not firm in its hole. did the tuner say something about ?

DOnt use your "tuning tool" it can make more trouble. if your piano does not stay in tune you will need a decent tuning hammer or a devoted tuner

It also cn be the screw that regulate the jack stop rail that touch the backcheck on return.

Yes, we discussed that the piano potentially might not hold its tune. He said some pins are already hammered deeper into the pinblock. That F2# after we tuned the right string of it, seems to hold the tune for now, and all the keys seem to be holding the tune, maybe it's too early to tell. Maybe the tuner forgot to tune that key ...
We agreed that we might later need to reinstall some tuning pins if the problem persists.
The piano stills needs a lot of work.
I wish I had a tuning hammer, but it's not like I will be tuning my piano from now on, I just needed to adjust that one string until I can have the tuner come and check it. So I don't know if it's worth acquiring one.
The piano is from the times according to my tuner when Riga used to make higher quality instruments than later on, the action is actually by the Red October factory. It has a keyboard of only 85 keys, not 88 (A0-A7)

The piano may not be worth too much work.

Pin hammered are not always easy to tune, the problem of your tool is that it can marr the edges of the pins then it became even harder to tune even with the good tuning lever. (and that can be a real problem to take out the pin to change it or repair it)

Did you find that tick ?

Jurgen if this is the only piano availeable, changing a few pins is not really a problem. What could be is if a line of pins are not holding, meaning there is a crack inside the pinblock.

Sure by German standards it is not a piano of much value, but as long as it is not worn out I understand the desire to have it in shape.

Probably not necessary to change the hammers for instance, but if the tuner know how to voice and regulate he can rise the musicality to an accepteable level.

I have no idea of the "good era" or other, not knowing those piano brand. Sure if the pinblock is loosing its resiliency,
no need to spend much money . But no reason it could not hold the tuning if the tuner know his job well

I'll bet that somewhere in side the piano is a little square piece of felt. I would expect it to be red color or maybe green color.

I bet for green ! how much do you put ?

I haven't had much time to investigate it.
But also the sheet music stand's hinges are buzzing (resonating) on some notes, especially in the middle octave and it's so annoying. I tried tightening the screws, I tried loosening them, didn't help

it is the axis of the brass part that have some play. usually a new one make it, or bend slightly the old one before reinstalling.

you also can try to close the outer part with pliers, or plier plus hammer, so it is closer

Yup! I'm gonna go with that opinion. The ailment descriptions don't sound good.

I will add some fuel to the fire, by saying that my piano tuner has told me that he tried some upright pianos in a music store and he said that a ~12000USD costing C.Bechstein would start to get close to my piano sound wise, which I bought for ~150USD, plus $65 for transportation and about $95 for the first tuning/regulation
So for me it's worth investing in this piano, as long as it's less than $11690, I've always wanted a Riga and I'm very glad that I bought one. We have completely different pianos available here from the ones that are available in the US/Canada.
Someday I will buy myself an Estonia grand, as the factory is only about 500 miles away . But for now I have what I have, I must work around it.