I think you were lucky they didn't clamp your car - or tow it away!
From what you say I assume the road is a private road, as otherwise the company would have no right at all to impose penalties for parking there. Are there any notices at the start of the road (which you would have driven past) which make it clear it is private? If there are - & if they are visible at night - you might be faced with an argument that you should have realised from them that you were trespassing. [I'm not saying I agree with this - my own view is that these clamping outfits are often bullying sharks - but it is as well for you to be prepared if the point is raised.]
Yes, unfortunately, these people can get your details from DVLA. In my view this is a breach of the Data Protection legislation but unfortunately the powers that be are more interested in the money DVLA get for providing the details.
Because of this, you are likely to get further contact. If I were you I would not ignore it. One letter, sent by recorded delivery (keep a copy) should set out all the reasons why you will not be paying - in particular that there were no visible signs anywhere near where you parked. Then, if they decide to take you to Court you can provide a copy of the letter as proof that you did not ignore them, & it will in effect be your defence because it will state your reasons for not paying.