Most of the early development work on using tank testing was done by William Froude (1810 - 1879). He was a long-time assistant to I.K. Brunel, initially working on the Bath and Exeter section of the Great Western Railway. Later, he assisted with the mathematical calculations on the Great Eastern and did a mathematical analysis on the rolling of ships, the results of which stood until the late 1970s (it took computers to beat this guy!)
In the early 1860s, Froude was elected to the British Association with a specific remit to study the performance of steam ships. At that time there was no way to estimate the power required to drive a ship at a specific speed. A lot of work had been done using both models and full-scale ships but the results were "embarrassing and expensive mistakes". Froude opposed an initial series of trials using full-scale ships under tow. He was alone in believing that model testing could provide some answers to the puzzles the architects were facing.
Pretty well everybody else disagreed with him; all the model work to this date had proved nonsensical since the researchers had failed to realize the complexity of resistance to motion of a floating body. This problem was cracked by Colonel Beaufoy of the Society for the Improvement of Naval Architecture who showed that the various resistance components of a ship hull all behaved differently (he did the tests in Greenland Dock, Greenwich).
In 1867, Froude did his model tests using models of two different hull shapes (called Swan and Raven). Each was built in 3ft, 6ft and 12 ft sizes. He did the runs in Darmouth Creek and observed that when models of either form were run at speeds proportional to the square of their length, they generated virtually identical wave patterns. From this, Froude was able to show that wavemaking resistance was proportional to the weight of the model when run at this corresponding speed. This became known as Froude's Law.
Now we get to the relevant bit. On 24th April 1868, Froude wrote to Edward Reed, the Chief Constructor of the Navy, proposing the construction of an experimental tank and outlining a two-year research program. In February 1870, their Lordships approved the expenditure of 2,000 pounds on the tank to be built in the grounds of Froude's house, Chelston Cross in Torquay.
A prominent part of the work was dragging flat planks of varying shapes through the water and also repeating the runs using surface finishes of varying types. In an earlier post I suggested an experiment to another correspondent which involved taking a 2 foot plank of 4 by 1 timber and cutting it to different degrees of fineness, retaining the 6:1 length to beam ratio. This was, in fact, a simplified version of Froude's work.
Froude's ideas were great and simple. he showed that the resistance of a ship could be calculated by (1) determining the resistance of a plank of wood of the appropriate scaled dimensions, (2) determining the frictional resistance of a model of the hull (3) subtracting (2) from (1), (4) determining the residuary resistance of the hull by multiplying (2) by the ratio of the weight of the model to that of the real thing and finally adding (3) and (4). By the standards of the day, it worked. It was now possible to make rational comparisons of one hull form with another.
The tank at Chelston Cross was the first properly-instrumented testing tank in the world. It was later moved to Haslar (in 1886) where it remained in service until 1938. Froude's son Edward remained in charge of the operations for 40 years after his father's death.
William Froude did a lot else; he showed the importance of interactions between hull form and propellers, designed much of the instrumentation, came up with the idea of the bulbous bow and, ironically for the man who made tank testing with models work, showed that there were scaling factors between models and real ships that couldn't be explained (and still can't). His work also showed that there were hydrodynamic factors in hulls that simply could not be explained away.
It is fair to say that every ship in the world today owes its performance to Froude's insight and painstaking work. He steadfastly refused to accept any payment for his services.
On other points, yes it is the same tank and models are frequently self-propelled. it depends what we're doing the trials for. Towed models are better for resistance measurements; powered ones for sea-keeping trials (you have never lived until you've seen a tank-typhoon).
I think the history of Froude covers Question 2 - the size of the model isn't so hot but the size of the tank is - as you point out, the last thing we want is interactions between the sides and base of the tank with the model.
Finally, the skeg trials are fascinating - they have different results
for every series that were run. It seems that the operator has as much
influence on the results as the design of the skegs themselves.