For the first issue,do you have a sunroof?
It could either be blocked sunroof drains,or more likely,blocked drains from the scuttle panel.Check the area around the corners of the scuttle panel under the windscreen for leaves and debris.
The second issue could be anything from a sensor fault to knackered plugs or the battery is on its way out.
Does the car have a full VW service history,so you can look and see when the plugs were last changed?
If you know someone or a garage with Vagcom or a diagnostic reader get them to plug it in and see if it returns any fault codes.