There are a few types of plastic that are not suggested for use with foods or water, and a few that cannot take the UV of sunlight for any length of time (years), but by and large, the big tubs are excellent homes for fish. If it is a Rubbermaid brand one, then you are fine.
Yes - fish can happily live in a tub all their lives. In many countries, a fish will live in a large (50-200 gallon) tub on the patio of an apartment. I have visited apartment where there are 10 stories of patios - each with a tub of fish on them! Most HOB filters can fit over the side of a tub, and a cannister or homemade filter is also easy to adapt to use.
My favorite fish for in a tub (viewed from above) are the ranchu, celestial, bubbleeye - for they look sooooo cool from above. A nice butterfly demekin is also impressive from above.
The easiest way to determine volume of a tub is simply to take an old milk gallon jug and fill the tub with a gallon of water at a time and count them. Or - if it is really big, you can use a 5 gallon bucket and count the buckets. I have a 5 gallon bucket I measured and marked in gallons with an indelible marker. I can measure water quantities very easily that way.
Enjoy your tub!