Database Mirroring - Will forcing the service only lose non-committed data? I have a database mirroring session in high safety mode between Server1 (Primary) and Server2 (Secondary)

According to this, synchronous data mirroring means


  every transaction committed on the principal database is also
  committed on the mirror server, guaranteeing protection of the data.
  This is achieved by waiting to commit a transaction on the principal
  database, until the principal server receives a message from the
  mirror server stating that it has hardened the transaction's log to
  disk. Note the wait for this message increases the latency of the
  transaction


With this in mind, if I lose Server1 completely (and irrecoverably) and force service onto the secondary using

ALTER DATABASE [MyDatabase] SET PARTNER FORCE_SERVICE_ALLOW_DATA_LOSS


Would I only lose the transactions that were in-flight on Server1?
Correct, once the Primary loses connectivity with the Secondary (closes), all in-flight transactions will be rolled-back on the Primary and never make it to the secondary.  The committed transactions are guaranteed to be written to disk on the mirror server in that mode.

Here is an excellent article with more detail on this subject - 
https://www.sqlskills.com/blogs/paul/a-sql-server-dba-myth-a-day-130-in-flight-transactions-continue-after-a-failover/