My guess (and only a guess) is that the number 400 means 400KHz. As Nigel says, 455KHz is the popular value, but I reckon your device is probably 400KHz.
G may be tolerance, temperature range or something else.
945 may be relevant to manufacturer only, maybe date code, probably unimportant.
How about a clear picture so we can see manufacturer logo and number of pins?
Google search turns up nothing similar for 3-pin resonators - have to give up there.
Failures are rare, other than bad solder joints or mechanical damage. Cannot see solder joints, but looks mechanically good (no cracking of blue coating)
Do you have an oscilloscope with 10x probe to check each outer pin (centre = common) with battery connected?
No, fairly obviously - imagine you need an object that's 455cm to fit in a particular 455cm hole - why would you imagine an object that's 3580cm or 12000cm fit in the same hole?.
You're unlikely to find a suitable resonator in a store, but you're also VERY unlikely to need one - they don't fail.
In my previous career as a TV service engineer I've repaired many hundreds, probably thousands?, of remotes - the only faulty resonators I've found were from dropped remotes, where one (or more) of the pins have snapped off due to the physical shock. Repairs consisted of either soldering a piece of wire to the snapped pin (you can 'mostly' find enough to solder to), or fitting a replacement resonator from a scrap remote - they all seem to be pretty identical.
I have tried to determine why is my remote for Sony TV broken, but I can't quite figure it out. I have tested almost every component with multimeter, they seem to be ok. I suspect that chip 34286g2 could be faulty, I tested all leads and they show 700 ohms resistance, but maybe something else is...