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(1) The PSR-E models don't have "punch in" or "step" recording like the PSR-S models do, just basic "record as you play." If you want to make a correction or other change in something you've recorded, you must record that entire track all over again-- but you don't need to record all of the tracks again, just the track that you want to change. That's with the on-board song recorder, of course; if you're using an external program, then you can certainly do "punch in" or "step" recording if the external program supports it.
Now, if you want to play along with a Style but want to play with both hands instead of having to use your left hand to control the chord changes in the Style, what you could do is to record a User Song but don't try to play your part of the song, just record yourself controlling the Style using the same section changes, variation changes, and chord changes as you want the song to contain. That might be a little tricky as far as counting bars in your head-- unless you're good at hearing the music in your head-- so another possibility would be to record the Style as well as a simple right-hand part to help you keep yourself straight about which bar you're playing. Then you can delete the right-hand track (which is probably Track 1) but leave the accompaniment track (Track A) alone. The manual should have instructions on how to erase a specific track of a User Song.
Now you can play back the User Song and the keyboard will play back the Style you had selected, complete with all of the section changes, variation changes, and chord changes you'd recorded, leaving you free to play along on the keyboard with both hands, or play along on your sax, or just run around and dance to the music, or whatever!
However, as far as actually controlling the chord changes of a Style in a manner that doesn't require recording everything in advance-- such as by sending chord change information to the keyboard from an external MIDI device or computer-- unfortunately there's no way to control the Style playback that way as can be done on the PSR-S models. What you'd need to do is record the Style to MIDI tracks in your DAW-- complete with the desired section changes, variation changes, and chord changes-- and then create loops in the DAW so you can repeat some desired portion of the recording for as long as you want before letting playback continue to the rest of the recording. If you've got an iPad, you could try using Cubasis to do that, or maybe Yamaha's free Mobile Sequencer app.
(2) You should be able to use the keyboard's Transpose feature to transpose the entire keyboard to whatever key is easiest to play and record in. The song will be recorded in the transposed key, not the key you're actually playing.
(3) The PSR-E433 doesn't have a feature to convert a recorded User Song to an MP3 or WAV audio file, so you'll have to just connect the keyboard's audio out (or PHONES/OUTPUT jack) to the computer's audio in, play back the song, and record the audio on the computer while the keyboard is playing back the song.
