BREXIT: Clearing immigration/customs @ LHR and onto Munich?...

Nothing has changed. Great Britain is still part of the EU. They are still in the negotiation phase on the withdrawal. It will be a few years before you will see a change.

Once we clear customs/immigration at LHR, do we have to again do anything "extra" on arriving in Munich?

Assuming that you are only transiting through LHR, you will not go through immigration or customs in the UK. The UK is not party to the Schengen Agreement. At LHR, you will stay airside, follow the flight connections signs, and go through a security screening where they will check your ticket and passport (ID).

Immigration and customs will take place on arrival to Munich.

The UK has not yet left the EU, target date is March 2019, so NO CHANGES.

The question always asked: Is this one through booking or two separate tickets?

If it is on one through booking, what Laura says is correct, you stay airside in Heathrow, and only go through immigration at Munich.
Customs is never an issue. Customs is the check on the contents of your luggage, you never go through customs, they only stop about 1& of people randomly.
If this is two separate bookings, you will have to go through immigration at LHR, enter the UK, pick up your bags and check in again for the second flight. You would then exit the UK. This would obviously take a lot longer.
In both cases you go through Schengen Area immigration in Munich.

Thank you. Very helpful. We have not book the 2nd leg (LHR to Munich), so it would be a separate ticket (TBD), so the last question would be how much time is needed between flights at that point. We land LHR @ 11:30a and there is a 13:50 Munich flight. We only do carry on, so no bags will be checked. I think thinks gives us enough time?...

Even if the UK accomplishes a break from the EU, for non-EU citizens, nothing will change, the UK never participated in the Schengen Agreement and open EU borders only applies to EU Citizens and products, so Non-EU Citizens always were subject to Border Controls entering and leaving the UK. You are not however entering the UK if you stay Airside, just head to the "Connecting Flights" passage rather than into the entry hall.

Even with separate tickets, you should be able to stay airside since you do not need to pick up checked bags. The times you indicated for arrival and departure are fine, you may have to go through security though. Just be aware that a missed connection means you are stuck in London and would need to purchase a last minute ticket to Munich, not sure the reasons you did not just book through to Munich, but too late now for that. You might allow a greater buffer between flights though, in case your arrival is late or you do wind up needing to go through immigration.

Heathrow makes it very easy for you. Go to this website:

Heathrow Flight Connections

Plug in your flight information and it will give you step by step instructions on what you have to do.

We have not book the 2nd leg (LHR to Munich), so it would be a
separate ticket (TBD), so the last question would be how much time is
needed between flights at that point. We land LHR @ 11:30a and there
is a 13:50 Munich flight. We only do carry on, so no bags will be
checked. I think thinks gives us enough time?...

That's a tricky question. When we travel on separate tickets, we typically do this at Heathrow or Amsterdam and allow 4 hours to compensate generously for flight delays from the US. We do what we can to limit the risk of missing the separate flight because if our inbound transatlantic flight is late and we miss that flight, the entire ticket from the second airline is therefore forfeited and we would be forced to buy a new roundtrip intra-European itinerary at the airport.

So it's up to you and how much of a risk taker you are. If you don't have to change terminals at LHR, that's even better. Like you, we avoid checking in luggage.

I assume many of the two ticket travelers are using frequent flyer miles for the home airport to London leg as there are often more seats available on the frequent Heathrow routes.

Why are people buying 2 tickets for a single itinerary?

Price.

We saved over $500 each flying JFK - AMS on Delta and then AMS - GVA on EasyJet than flying nonstop on Swiss or any Delta code share to GVA.

And it can also be a false saving. We had never had it happen in 20+ years of travel but last year we had a Lufthansa flight from Denver to Frankfurt canceled and, of course, we missed our easyJet flight to Edinburgh. And when we finally got there three days later, had to buy additional tickets at full price. While the probability is low, it is still a possibility. We have changed our opinion about non-connected segments.