Air ticketing is a bit more nuanced than merely finding some flights you want to travel on. In some sense, that is the easiest part of the ticketing problem to solve. The difficult part is finding a way to price a given journey, and the hard part is finding the cheapest way to price it.
On the airmiles question ...
(so I can use airmiles for that leg)
BA doesn't permit you to buy a ticket for which one leg is Avios and another leg is revenue. You can use Avios to reduce the cost of a revenue ticket, but you can't buy one leg with Avios and another leg with cash. It isn't how the scheme works.
BA also, in common with all airlines, only allows you to redeem airmiles on its own flights and on the flights of its partner carriers. You can redeem Avios on all oneworld carriers and a number of non-oneworld partners.
I think the best you can do with Avios, unless you split the ticket, is something like LHR-BA-HEL-AY-MSQ, for which there is no revenue fare (which is why it doesn't appear in ITA Matrix) but it should be a valid Avios redemption. The taxes may be higher than what you expect because the Finnair (AY) leg will remove the tax/fee cap, which may obliterate the Avios saving.
There is only two flights per week on HEL-MSQ operated by Finnair (AY); one on Tuesday and another on Saturday. BA's redemption finder doesn't even recognise MSQ as a valid airport, so you'd have to book this by phone. You'd be better off finding availability on the HEL-MSQ leg on AY's website and separately finding availability on the LHR-HEL leg on BA's website.
On the why doesn't ITA show arbitrary routes question ...
The first thing to realise is that ITA Matrix will only show journeys which are purchasable on one ticket. That is a strong constraint.
BA and B2 have no interline agreement.
I get a few options ... but not the Belavia one. Am I missing something obvious?
British Airways and Belavia do not have a ticketing interline agreement.
That means there is no contract between these two companies to honour each other's tickets as legal documents with financial value. Therefore if you arrive at a British Airways flight holding a ticket (or e-ticket) issued by Belavia for continuing travel onto BA, British Airways has no legal way to be sure that Belavia will pay it for the transportation. And vice versa.
The additional complication with electronic tickets is that one airline may not even have the necessary back end systems to communicate with the other's e-ticket server.
So, no one can sell you a connecting flight between these two carriers.*
Very limited set of fares covering this route that allow travel on BA.
You also have to find a non-empty set of fares that will cover your journey, and satisfy the validity constraints of each fare in that set. Every fare comes with an associated set of rules specifying the conditions under which it may be used, including which flights it can cover. The geometry is, every flight must be covered by exactly one fare, and each fare on the ticket must cover one or more flights.
In most cases, at least one return fare will be published on the city pair, and it is easy to use that fare for pricing your journey, even if you have to use several different planes and carriers to get there.
British Airways itself has chosen not to publish any fares on LON-MSQ, so you have to cover these flights in a different way.
The fare you found via Frankfurt but starting on BA looks to be Lufthansa's
YFF77WW fare on LON-MSQ. This is a "full Y" fare, i.e., the most expensive and most flexible type of economy fare that is available. Generally air carriers prefer you to travel on their own planes or maybe their partner's planes. They do not typically sell transportation on their competitor's planes. For instance, you could not use Lufthansa's cheapest fare (called
K04LGTE3) to travel on BA from LON-FRA because of the following restriction:
THE FARE COMPONENT MUST BE ON
ONE OR MORE OF THE FOLLOWING
ANY LH FLIGHT OPERATED BY LH
ANY LH FLIGHT OPERATED BY OS
ANY LH FLIGHT OPERATED BY LX
ANY LH FLIGHT OPERATED BY EN
ANY LX FLIGHT OPERATED BY LX
ANY LX FLIGHT OPERATED BY LH
ANY LX FLIGHT OPERATED BY OS
ANY OS FLIGHT OPERATED BY OS
ANY OS FLIGHT OPERATED BY LH
ANY OS FLIGHT OPERATED BY LX.
[ Note: LH = Lufthansa, LX = Swiss, OS = Austrian, EN = Air Dolomiti. All these carriers are owned by the same company, the Lufthansa group. ]
In this case only Lufthansa's most expensive and most flexible fare permits you to fly on BA metal for part of the journey (and I think you would struggle to find any agent willing and able to sell this ticket anyway).
The alternative is to construct the price by gluing several fares together, for instance, a fare on LON-MOW + a fare on MOW-MSQ. You must travel via the point of combination; in this case, via Moscow. This is what ITA Matrix does if you force it to price with BA first and then go through Moscow. (It uses BA's LON-MOW
Y1 fare and SU's
BFO fare on MOW-MSQ.) But again, fares generally don't allow themselves to be glued together like this and only the most expensive fares in the tariff allow it. These rules are set out in the Combinations category for each fare.
Any-airline ("YY") fares could once be used for this kind of trip, but they were withdrawn from sale last October.
Between 1945 and 2018, IATA published "YY" fares or "Any airline" fares that were valid for use on any airline, within some mileage limit, for travel between the two points, without other restrictions. Originally, it was the main way to buy travel that required multiple airlines. Even reservations were not required; the carrier was obliged to accept you if it had seats available at time of check in. However, since e-ticketing became universal, a number of carriers stopped accepting tickets with YY fares. Unfortunately, that included both BA and LH. However, these fares were very expensive, and were so unpopular by 2017 that IATA decided to stop publishing these fares anyway.
You could use a "hacker fare" to fly this trip in whatever manner you like.
No one can stop you buying two (or more) separate tickets for this journey, on exactly the flights you want, which is sometimes known as a "hacker fare" by over-excited travel portals. You could buy one leg on Avios and a separate ticket for the rest of the journey. However, the possibility of luggage interlining between the separate pieces of your hacker fare is very low, and in the event of any disruption or rescheduling of your flights, it will be up to you to repair your trip proactively, possibly by purchasing new tickets.
I suspect the money saved on the Avios is not worth the effort and the risk.
* This isn't entirely true as stated because it appears that a clever travel agent could use a third party airline trusted by both BA and B2 to act as the ticketing carrier. In practice, using the third party to evade this restriction this would probably be considered a violation of the agent's ticketing authority by all three carriers.