If I have two pieces of unknown alloy, such as 2 lb of BHN 7, and 1 lb of BHN 14 and melt them together , what will be the BHN of my final mix? Can I do a straight proportion to get a final BHN 9 ?

Yes. Straight proportion

7 BHN * 2 lb = 14 BHN-lb
14 BHN * 1 lb = 14 BHN-lb

(14 + 14) BHN-lb = 28 BHN-lb

28 BHN-lb / 3 lb= 9.33 BHN

there seems to be (at least in my testing) one variable in it. That's tin. Alloys like 20-1 that get there hardness just from tin don't seen to make an across the board exchange with alloys using antimony for hardness. If I have 20-1 (lead/tin) that lets call 10bhn and add it 5050 with an alloy that is say 20 bhn and youd think youd end up with a 15 bhn alloy but usually it will run around 13. Also if you don't have a lead hardness tester you cant count on your alloy being a set bhn. Ive seen what people call pure go from 6 bhn to 8 bhn and have seen wws go from 9 to 13 and what people call linotype, Ive seen anywhere from 17 to 30. But for most of us plain math is close enough. Even hardness testers can goof you up. Ive got a cabin tree and an lbt and had a Seaco. Each one of them read slightly different. So what your getting is a reading + or - about 3bhn. I use my testers more to compare alloys I have then to put a wrote in stone bhn number on an alloy.

I got lucky a few years back. My wifes uncle owned a large print shop in Columbia Missouri. He still had linotype sitting in his basement from the early days when he retired. I also had a good stash of almost pure lead from my days as a telephone co. cable splice. I mix it one part linotype to to 10 parts lead for use in rifles or 2,000 fps+ and mix it 1/20 for most handgun shooting up to 1500 fps or so. No need for gas checks and never get any leading.

That being said, a pure lead bullet in a pistol with a gas check running 1000 fps out of my 45 Colt or 44 mag will do more damage to a deer at bow range than those hard bullets running 1500fps. Those hard bullets (about 24 BHN) act just like FMJ bullets. Number 2 alloy(the old lead wheel weights and a dose of Unique) is about perfect at 1200 fps with a gas check for deer size game. No 2 driven any faster in my two deer revolvers results in lead in the bore.