There was considerable evolution of piano design, from the first 1720 Cristofiori to the later 19th c. Erards and Steinways. The strings got longer, and thicker, the hammers and soundboards heavier, the frame heavier and stiffer. The piano wire also went from iron to steel, and different metal wraps were used on the bass strings, and the scaling ( the various lengths of the strings) also varied. You can get an idea of the general effect listening to some good recordings of fortepianos, vs modern ones: fortepianos have a somewhat smaller dynamic range, less sustain and brilliance in the treble, slightly less clear bass...that's not to say they sound worse- they perhaps have more charm and intimacy , compared to a modern big concert grand.

What pitch was used is a very complicated question. Once higher-tension steel wire was available, in the earlier 19th c., there seems to have been a lot of variety of pitch, sometimes lower than the modern A=440hZ, but sometimes actually higher. It not only varied in time, but by country: here is a nice summary. For historical performance, these days, the norm is to play at a lower pitch- a Mozart concerto with fortepiano will be lower...but although Gottschalk , in the 1850's, probably played at a higher pitch, perhaps A=444, you never hear that.

As far as temperament- which is what perhaps you mean by "interval"- it was a very big issue in the 17th and 18th centuries. The central problem was obvious: if you want to play in many keys, the notes are easily not going to be interchangeable. If those keys are few , with only a few sharps or flats in the key signature, the compromises are somewhat manageable, and there were a variety of solutions, most of which we now call meantone- and you can hear them on harpsichords today. By the time the piano really became very important, after 1790, though, more music was being written in more keys and with complex harmonies and by the mid 19th c. equal temperament had become pretty standard. The great acoustician Helmholtz would complain about it, and there would be attempts to create keyboards that had different keys for, say A# and Bb, but it was really the most practical solution. He was right to grumble: the major thirds are too wide...but although guitarists could have tweaked their guitars into meantone when they "warmed up" a chord while tuning, and singers and fiddlers could compensate in that direction as well, regular keyboards were kind of stuck with one note per key. Isacoff's Temperament: The Idea that Solved Music's Greatest Riddle is a very nice book on the subject of temperament- which can get complex. People still tinker with various tunings. There were a series by Werkmeister, "well temperaments", in the late 17th c. that may have been used by Bach ( though his Well Tempered Clavier could have been equal) and, who knows, might have been tried by someone tuning for Mozart, and sometimes are still tried. It should be noted, too, that 20 + years ago Lyndon Larouche added abolishing equal temperament to his political platform, so there are some really passionate rants out there against it.

One aspect I am not sure of is the modern "stretching" of the tuning on piano. The high overtones of the bass strings are, actually, sharp to the fundamental pitch. That means that the lowest strings on a concert grand actually are generating frequencies that would be sharp to the highest strings, if everything was tuned at one pitch. The solution to that is to make the upper strings slightly sharp to the lowest. I am afraid I don't know when exactly that started to be done- on a fortepiano, it might not have really been much of a problem, given the less bass was less brilliant.

Yes, it was different, in several ways.

As it was already mentioned, neither the reference pitch nor the tuning system were the same. Also, the instrument AND the techniques employed by the people tuning the instruments were different. I can comment on those things if you have more specific questions.

You might find this old answer on local pitch customs from /u/erus helpful.