Yes.

Sample size and sample rate are two different things. Don't conflate them.

More bits per sample can mean a lower noise floor. This can mean less noise when amplifying the digital signal. But at a certain point other sources of noise, like pre-amplifier noise, microphone self noise, and environmental noise will dominate over the quantization noise of sampling.

A higher sample rate can encode higher frequencies, and mean a more accurate representation of high frequencies, especially when when resampling.

96k rate is pointless. record at 48k. however 24 bit IS better than 16. It becomes noticeable when you listen to the decay of a sound. They are much smoother with 24 bit recordings. The typical example is a cymbal crash. The tail of the signal sounds noticeably better with 24 bit. ergo 48k/24bit.

There are reasons to record at 96k when you are doing real time monitoring of the digital signal. This is because your buffer delay can be lower with 96k. For film making this will likely never be important.

I respectfully disagree that the bits will lower the noise floor

I should have said it can lower noise, not really the noise floor - specifically, quantization noise. It's perfectly possible to get enough SNR with 16 bits, if the signal is strong enough. Bits do not equal gain. Every added bit means the quantization noise is 6 dB quieter, which means you could lower the gain by 6 dB and achieve the same SNR - at least if quantization noise is the dominant source of noise. As the quantization noise becomes quieter and quieter with more and more bits, at some point some other kind of noise is going to dominate, e.g., the pre-amp's noise. That's why you don't see recorders with 32 bits very often. You could make one, but the extra bits would just be wasted encoding the pre-amplifier's noise. A good pre-amplifier can have more dynamic range than 16 bits can encode, so there are reasons to have more than 16 bits.

It's just a rule of thumb, and it's a pretty good rule if one uses it with care. For example, you would not want to turn the gain down 48dB in a 24 bit setup thinking that you will have 16 bits. Also, a 16 bit recorder typically records at 14 bits, unless you use an added resolution driver. So you can think of 24 bits as really giving you a 16 bit minimum, whereas, 16 bits will definitely not give you a 16 bit minimum under any circumstances. 24 bits will also allow you to optimize the 16th bit. So it is not, in fact, a choice of 16 vs 24, you don't get the 16 unless you use more bits. Once I was recording a rather large and expensive orchestra, and the Sennheiser MKH 800's drew too much phantom power from the converters. There were 36 mics, and, of course, most preamps really don't put out 48 volts anyway. The recording dropped 24 dB when the mikes blinked. Since it was 24 bit, I just cranked it back up the 24dB with no issues--well, very few issues. Now why that was true had also to do with the fact the mics and pres had very low self noise, but the extra boost room, no matter how you define it, was, shall we say, the saver of the day.
We all use the term "gain" in various ways. One can narrow the definition, but it basically means just means an increase, and that increase could refer to any number of interrelated factors. It used to be, you turned the knob, and you added, for example, voltage. Now, the gain or gain/trim knob or knobs can be a hybrid of analog and digital systems, or just digital gain. Turn the knob, it seems to get louder. Simple. But, then you must go down the rabbit hole of perceived loudness and so on. And to what purpose?
As far as dynamic range, a typical recording has a range of 60-70dB, so the number of bits is sadly completely irrelevant as far as dynamic range is concerned. Of course, after compression, the dynamic range is, well, compressed. In the current market, you either compress or you are out of work. 16 bits gives you 96 dB dynamic range, even more with noise shaping, way more than you need. And, in fact, all of the ads for converters about blah blah dynamic range is just BS. Transient response, OTOH, is more of a big deal. As is the design of the circuit. Needless to say, the other parts of the preamp will not go past 120dB without exotic physics, anyway.
But the main thing is that for a variety of really quite complex reasons, 24 bits is the way to go, until something better will come along.
Another way to look at it is that moving the microphone one foot will make more difference than any of the technical stuff.