Where did you read this? All the BBS drives run the same software, so no reason it won't work with all of them. If you don't fancy risking it, have a look at the Eggrider display, more expensive, but more functions inc. bluetooth if you like that sort of thing.
This photo may help you understand the clearance you need. You must have around 65mm between the centreline of the BB and the chainstay. This frame has around 64mm, so you would need 1-2mm spacer on the BB for the HD to fit.
Hmm, I'm sorry to say I don't think you are going to be able to increase performance with that battery, it isn't really a good match with Cornish hills where you are pulling high amps for long periods. You really need a pack with quality branded cells and a BMS that can supply 30amps con. to get...
You may be able to improve the performance of your existing hub by fitting a decent KT controller and LCD, but your battery needs to be able to supply the extra current. Do you know it's specs or have a link?
Jimmy at ebike batteries only uses quality branded cells and will collect and deliver your battery, give him a call, he's a very nice bloke and has an excellent reputation on here. He may be able to increase the capacity of your battery slightly for you.
No, not a generic one, but there are aftermarket batteries available for the Yamaha powered bikes, although some have given problems. There are threads on here discussing them, do a search. Or you could get your battery re-celled.
eBike Batteries
As peter.c says it may be ok, but from your photos your BB is deff. more than 73mm, so you will need a 100mm HD kit. You are best to strip the BB and take some accurate measurements to ensure you have the clearance on the chainstay. I will post some tomorrow when I'm home.
Post some photos of your BB with the bike inverted showing the chainstay on the drive side. A 68mm should fit your 73mm BB as long as you have enough clearance for the sec. gear casing. If not, then it's prob. not viable as the 100mm with spacers will cause chainline issues.
That is the newer style Freego battery which has a different base plate to the generic Silverfish case. A Silverfish should fit, check dimensions, but you would need to get one complete with base plate and rail.
If you are looking for lightweight with decent capacity this might be worth considering in 10S2P format as long as you are not running over 15 amp controller.
https://enerprof.de/en/ebike-batteries/softpacks/36v-10s-batteries/202/softpack-battery-36v-10ah-bms-20a-xlr-3-with-m50?c=10
What's happened to your old battery? 2 years is not long to be needing a replacement. If it's developed a fault, it may be fixable. I have seen 3 Freego batteries with bad internal solder joints causing total power loss that have just needed simple re-soldering.
I've run both BBS02 and HD through a modern 3 speed SA hub. Not clocked up crazy mileage, but no failures. Ok on the road, not really enough range for slow off road use, but fine on fast trails. Got a build on the go using the SA RX-RK5 5 speed hub at the mo for a better range of gears. AS VFR...