I think I found a satisfactory solution to the Samuel Quittner question. Due to the large amount of mistakes and inconsistencies in the records, I decided to look for better consistency at identificying their addresses. To my luck, I found the addresses much more reliable and I was able to better connect the dots, so to speak.
I first identified and seperated the two Samuel Quittners, which there indeed have been two. The younger one lived near the city center at Grosser Taban/Hauptgasse nr. 526. The older one lived on the outskirts at 542 and then 426. Also to my luck, I was able to find a map from 1848 and see that each house had a unique number not related to the street (https://maps.hungaricana.hu/hu/MOLTerkeptar/8697/) so I could ignore any inconsistencies in street names since Grosser Taban/Hauptgasse seemed to have been used interchangeably. Unfortunately, I wasn't able to read their professions based off the handwriting. Maybe you know more about this?
With the two Samuel Quittners seperate, I was also able to identify their wives who lived in the same address. And to my surprise, I found a Franciska Quittner living at the same address who was married to the elder Samuel Quittner and died in 1860. The death record shows her as "Wirths Gattin", so "wife of the tavernkeeper"? Which makes a lot of sense.
I then also saw that just a few months later the elder Samuel Quittner remarried to someone named Kunits/Baumgarten Theresia. On the marriage record you can clearly make out that it's the elder Samuel Quittner based on the address. You can also see that both had previous marriages and I'm guessing that Kunitz/Kunits was the surname of Theresia's first husband, which could actually be Kohn. That part is still a mystery to me and needs to be more properly investigated. I couldn't find any children but they were both quite old when they remarried.
But what really gave me the "aha" moment was Kati Quittner and Himmler Wilhelm's marriage record which not only mentioned "Fany Quittner" as Kati's mother but also pointed to the same address to where the elder Samuel Quittner lived. So then that gave me a kind of soft confirmation that this "Fany Quittner" was actually supposed to mean "Franciska Quittner", the elder Samuel Quittner's first wife.
So what really threw us off were:
1. Kati Quittner's mother is inconsistent among Kati's marriage and death records so one of them has to be a mistake
2. The coincidence of the similar names of the elder's Samuel first wife and the junior Samuel's second wife
3. The coincidence that both Samuel Quittners remarried at roughly the same time (just 2 years apart)
I manually combed the records several times and there was no hint of a "Himmler Zsofi/Sofia" who would fit the time period to be a mother of Kati Quittner, and the marriage record is closer in time and place to her real mother. So that leaves us with the best assumption that the correct mother is "Fany Quittner" and that "Fany" is actually "Franciska Quittner".
I also connected all the dots for the younger "Samuel Quittner Junior", who lived near the city center. His first marriage was with Friedmann Catharina whom we had many children with. She died in childbirth in 1858 and Samuel Quittner Junior ended up remarrying a younger "Fanni Quittner" who was born in Verbó, Nyitra (now Slovakia) with whom they had many more children with. But I was able to consistently identify that kids to both of these marriages were born to the same address, near the city center. There is a notable few year gap between the first wife's last kid (and her death) and the second wife's first kid, more on that below.
After I connected all these dots, the timeline of events (births, deaths, marriages) made much more sense. It also made sense that I was able to find records of these marriages actually occouring, since records were created from 1850 onwards so it would have been strange to not find anything of people who spent all their lives in Balassagyarmat.
Although I'd say I'm 80% confident about this interpretation of the records, there are still some missing pieces of this Quittner puzzle:
1. I was unable to find a marriage certificate of the younger Samuel Quittner's second marriage with Fanni Quittner in Balassagyarmat. We know for sure that Fanni Quittner was born in Verbó Nyitra, so it's possible they married there before moving back to Balassagyarmat? This is where the several year gap between the first wife's last kid and the second wife's first kid can be relevant.
2. I was unable to find the death record of the younger "Samuel Quittner" in Balassagyarmat either. Based on the records of his kids' marriages and wife's death, he must have died between 1869 and 1892. Maybe he died in a different location other than Balassagyarmat? Both of his wives come from Verbó, Nyitra and we don't know where he was born either. It's possible that we need to look at the records from Verbó?
3. Who the first husband of the elder Samuel Quittner's second wife (Theresia Kunitz?) is still a mystery. I haven't been able to find much. It could very well have been someone named "Kohn" who married a "Theresia Baumgarten". There's quite a bit of inconsistency on who the parents of Theresia were.
4. Did the first marriage between the elder Samuel Quittner and Franziska result in any more kids? Franziska died in her 40s, surely they must have had more kids. It's possible they all died young and we don't know for sure, since records begin in 1850.
5. This is perhaps more of a side track, but I found a "Jacob Quittner" who lived in the same or adjacent house as the the junior Samuel Quittner. He had a wife and many kids. Surely they were related in some way but how? Their parents had different names so it's possible they were cousins. We don't know because that qould require records from before 1850.
I have to admit, this type of detective work quite addictive. :-) Although I'm 80% confident about these assumptions, it's still some ways from being 100%. If you've got the time and energy I would really appreciate it if you could look over and make sense of all this information and either confirm or indicate that it's too insufficient to make an assumption.
Below are the links to FamilySearch for convenience. When tagging sources, I've made notes for the sake of convenience in the source titles on address, occupation and any info that was relevant.
Samuel Quittner elder: https://www.familysearch.org/tree/person/details/GRY9-KWT
Samuel Quittner junior: https://www.familysearch.org/tree/person/details/GRV5-1M7
Jacob Quittner, possible relative of Samuel Quittner junior: https://www.familysearch.org/tree/person/details/GRYS-QNC
Map of Balassagyarmat from 1848: https://maps.hungaricana.hu/hu/MOLTerkeptar/8697/
There's another Jacob Quittner as well, but not connected to any of the above names and did not share the same/adjacent houses with any of the aforementioned names:
https://www.familysearch.org/tree/person/details/GRY1-LZJ
Coincidentally, both Jacob Quittners died a year apart.