Use a text editor to open "customScripts/expansionsettings.gd", and find the line:
var swollenenabled = true
Change the "true" to "false" to disable most of the swelling and immobility, they may need to have an update triggered (ending the day if nothing else) before the change goes into effect.
Generally, the in-game solution is to give them a bath using the luxury rules, though that only works after ending the day.
Branding is not mandatory for slaves; according to the lore, it provides magical functionality to prevent escapes and (for the advanced version) enforce particular rules. You would not be alone if you are interested in distinguishing the social rank of your slaves, but nobody has invested time into implementing it and it is a rather broad mechanic to implement for a rather particular perspective. The Discord for this mod is a better place to offer your suggestions as most of the modders do not actively monitor this thread, but you can leave them here if you prefer.