Convert SWF to MP4

Yes. SWF has already discarded some detail and MP4 discards more, because re-encoding starts from what survived the first pass rather than from the original.

Not here. We can read MP4 but no engine of ours writes SWF, so this conversion only goes one way.

You can set the video codec, the quality or bitrate, how long to spend, ten-bit colour, the resolution, an exact width, how it fits, the frame rate, which way to turn it, whether to mirror it, where it starts and stops, the audio codec, the audio bitrate, the sample rate, and mono or stereo. Anything left on Auto is decided by the encoder, which is usually the right answer unless you are targeting a specific size or device.

On our server. The file is sent over HTTPS and converted in a sandbox with no network access of its own; your input and the result go together, removed at once if it fails and otherwise kept for a few minutes so you can download them, then deleted — whether or not you did. There are no accounts for anything to be kept against.

Yes — there is a per-file cap and an hourly job limit, because this runs on one small server. The API page states the limits currently in force rather than a number baked into this page.