These are all great questions! It's really fun to see the amount of thought you've put into imagining Razmani life and architecture. "Run with it!" is definitely a fine attitude for building upon what's in the wiki here -- there is lots of room for imagination, especially when people are describing how their character's own individual family/neighborhood/village lives, as opposed to making sweeping claims about WHAT ALL RAZMANI (or whatever else) DO. But since you had lots of interesting questions I'll give some more details about "typical" Razmani customs.
First off, there are two basic types of Razmani towns/dwellings. One of them is the style where the dwellings are excavated back into a cliff face, and their facades are elaborately carved to create different architectural elements of the sort one would normally find as part of a non-Razmani building's actual construction. The other style is where buildings are constructed on high ledges and beneath rock overhangs, with walls made from stacked drystone and adobe. These aren't necessarily mutually exclusive styles, and a big city like Alheri would have both. Generally speaking carved-facade buildings are most common to cities, and rock-ledge buildings most common to villages, but that's definitely not a hard rule. Both of these types of buildings can be found in any city where Razmani dwell in significant numbers, as they tend to live in custom-built enclaves apart from people of other heritages.
[Home Size] How common is it really for dwellings to "descend...into extensive complexes of subterranean chambers," is that usually reserved for more wealthy families?
A very extensive single-family excavated dwelling would tend to mostly be something for rich or prestigious people, who can command the labor through wealth or popularity or political position. Even these extended dwellings would consist of fairly small rooms, which might not seem as pleasant to an outsider but which, for a Razmani (as you suggested), would feel more cozy than cramped. Moreso than wealthy dwellings, however, extensive dwellings tend to be built by extended family groups.
[Home Density] Sort of related to (2) above - how "crowded" are typical Razmani households? Do they typically live with extended family, or do they spread out and as children grow older, they tend to live on their own?
Razmani families like to stick together. The fundamental unit is the nuclear family of wife, husband, and their children, but this is just the basic building block from which much larger and more complex associations are formed. Typically a Razmani family will have their own personal set of rooms, but these will be linked up with relatives' dwelling spaces by means of internal passages, and there is a great deal of visiting back and forth and sharing space. So the largest dwelling complexes tend to only occasionally be the property of a single family, and much more often are made up of several smaller related family units linked together. These complexes can grow larger through marriage, and while it is somewhat more likely for newly married couples to move to the home of the bride's family, if more or better building space is available with the groom's family they will often take up residence there instead.
[Home Layout] Are there notable features of a Razmani household?
Most Razmani prefer smaller rooms, particularly to sleep in, so bedrooms tend to be little more than narrow rooms with carved sleeping niches. Some homes, particularly more modest ones, will have both sleeping and storage niches all around the walls of a single larger room that itself functions as the main living space. It's common in larger families (and in Razmani-style inns) for multiple sleeping niches to be carved into the same wall, one above the other up to three high. It is a notable feature of Razmani houses that storage space is mostly "built-in". They also feature ventilation shafts for fresh air, and cisterns for collecting rainfall and runoff. Excavated dwellings can have rooms on multiple levels, and stacked-stone or adobe buildings are usually at least two-storied if not more.
The most favored casual gathering space is on rooftops or terraces, either connected to individual family dwellings, or part of a public space accessible by a whole community. Razmani love an opportunity for a view, and natural vantage points are often turned into communal gathering places. Most Razmani communities also have an indoor central gathering area, used for important political or ceremonial activities.
[Home and Work] Would Razmani typically have space in their homes to do much of their crafting work, or would they tend to want to separate the two?
Despite their love of cave-like spaces, Razmani actually like to be outdoors to do much of their work. What they like best is to work out on terraces, rooftops, and balconies. Sometimes these are connected to their own dwelling complexes, and other times they're part of a larger crafting-and-shops complex instead. These workspaces are often the same areas used for social gatherings, as many Razmani like to work in company or just be part of a broader social scene while at work. They will also work out of the open-fronted niche-like rooms along streets and walkways which most commonly serve as their personal shops, where they can simply raise or lower an awning to the outdoors depending on the weather.
[Connections to Other Homes] I can't help but imagine that in an extensive system of carved passageways, it'd be rather easy to have internal connections to neighbors, and I could sort of picture navigating a reasonable space of a Razmani-dominant city without even setting foot outdoors. Is that roughly lore-accurate?
This would definitely be accurate! Alheri in particular includes a lot of interior passageways to conduct people from one home to another, and between homes and places of business. These are typically Razmani-only features, while mixed Razmani and non-Razmani traffic travels along ground-level streets or outdoor pathways carved into cliffsides. Due to their strongly vertical nature, Razmani cities and villages also feature a great many ladders, stone-carved stairways, and even mechanical lifts that operate with a complex rope-and-pulley system.
Rostam wrote: Something that occurs to me when I read your post is the examples we have of cave-dwelling cities in Jordan, particularly Petra.
Although they're a fairly Avaria-unique people, part of Razmani culture and history is in fact based on the Nabateans and their rock-carved cities like Petra. There's a really great look at Petra and its construction and hydrologic engineering in the PBS Nova episode "Petra: Lost City of Stone" (2015); highly recommended if you can find it online!