Heck yea, you should have an anti-sway device with that very short wheelbase Liberty!
i pulled my popup with an Explorer and still got sway. would never pull a trailer without a sway device, with a Liberty.
as far as the water, should've open the faucet valves before folding the trailer up. you may not get all the water out.
but you should post this part of your question, in the Popup section here at FRF, since it's a popup-specific question.
and Zoe the Wonder Dog(R.I.P.)
'07 Roo 23SS pushing an '07 Chevy Avalanche
Equalizer WDH and Prodigy BC