Does SQL Server execute queries in parallel? Does SQL Server execute queries in parallel?
In other words, if I run a heavy query that takes 10 seconds to execute, and at the same time start another heavy query that takes 10 seconds, will the second query actually start after 10 seconds, or will they start both at the same time?
You mean "concurrently". The answer is yes, with caveats that are too broad to discuss here.
In fact, the whole point of RDBMS is concurrency.

"Parallel" has a precise meaning in SQL Server: "a single query is distributed over more than one processor core".