The spring actiin in the lever is normal for some of these big actions but I think was only incorporated on the large actions and not the medium or small ones.
All of these 1902 patent rifles were nitro proved and I would think that the Hornady ammo would be fine.
Also, I don't think that Kirton has had the opportunity to personally handle every rifle listed in his books and the lack of comments on it may just be due to the lack of more info on the Webley ledgers.
It is common for the Webley retailed 1902 rifles of their own to just have their trademark and patent information on the side as they were the makers of the entire rifle regardless of who retailed it be it Army & Navy, Rigby, H&H or whoever.
I say this of course knowing that some makers would stock, engrave and sight Webleys to their own style but most you run across will be very similar to yours.