An English Tom Thumb is a lovely bit and most horses go really well in it. If she is a little heavy then plenty of transitions between paces and within the pace will help her develop her balance better, also use with lots of circles, serpentines and loops to improve suppleness.
I've also seen short shanked pelham bits be called english tom-thumbs. That bit would not be considered harsh where I live because it's short shanked and double jointed, but the gag action does add to it. It's no where near as severe as some of the crap I've seen on some horses.
I know it's not exactly a fullmer, but it sure looks like one with shorter cheek pieces. I'm quite well versed in bits, but different countries have different terminologies sometimes.
No definitely not a dog bone gag! - study the shape and note that there can be no gag action for this bit!
This is a dog bone gag bit - the dog bone refers to the small link in the middle that is shaped like a dog bone. UK name for that link would be French link.
The Tom Thumb (English) does not look like a Fulmer except that the rings are outside the cheeks, they are a totally different shape, are shorter and are not used with keepers. I'm extremely well versed in bits being a Pony Club 'B' certificate examiner, BHS Stable Manager and been teaching students for exams for decades.
The bits are as named. The Tom Thumb you have a link for is the American Tom Thumb. The majority of bits excluding the Western bits are all based on the English names. Their names go back decades if not centuries.