Hi Jack
1.- Yes, in this case FITS is the best option. Unless it is a very large image, always use 32bits for processing. It may be a lot more than needed just to store data, but makes things much better when working the data. Additionally, many processes in PixInsight will use internal 64bits accuracy when handling 32bits images.
2.- The answer to this question will generally depend on the software that you are using. In PixInsight there is no need to worry (as long you don't close the image). Views (images loaded into Image Windows) are independ objects from image files. This means, if you use the "Save as" option to write a new image, with a different bit depth, this will not affect the depth of your View. Similarly, if you write an image in JPEG lossy format, you won't get any artefacts from the compression, because the view is not affected by this operation.
The only way to change the bit deph of a View is to use the SampleFormatConversion process.
Having said that, if you open a jpeg image, certainly you'll be able to write it as even a 64bits image, if you like. But, you'll have only 8bits of real data. Indeed image processing may increase the number of levels, but the data loss is unrecoverable.