These Disc Jockey things do tend to suffer turntable rumble; a spot of grease will help but may not eliminate it altogether.
The speed problem won't be caused by a sticking auto-mechanism as that disengages totally until the end of the record (well it does on other record-players anyway, but this is Philips
).
Give it an aural test followed by a stroboscope test and see what the outcome is.