Can someone help me with some knowledge gaps here...
A. How can Biden win, but lose the Senate?
B. Am I right in thinking the Senate is kinda like our House of Commons, and the House is like our House of Lords?
Not all senate seats are up for re-election, and in those states where there is a senate election usually (but not always) the candidate that wins the state is more than likely to also gain a senate seat. But people in each state, could, in principle, vote for a Democrat president and a Republican senator (or vice versa). You don't have to block vote. Traditionally, in the senate, some states have these old "stalwart" senators who have been in office for 4+ terms (1 term = 6 years). These stalwarts (Biden was one of them in Delaware; that ass McConnell in Kentucky is another; Paul Simon--retired--was another from Illinois) can in fact, get voters to switch allegiance. So it is entirely possible that someone could vote for their incumbent stalwart, just on the basis of "they like him and he does a good job and has been around for along time" while voting for a different party's presidential candidate in the same election cycle. But the most important factor is that not all senators are up for reelection en masse.
(If the above makes any sense, I'll be impressed, because I'm totally piss drunk).