You should get out more ~ try asking the natives these questions.
Neeps are Turnips or swedes, mashed with butter, salt and pepper.
Heavy is one of a range of brews. Think of it as Bitter rather than IPA which is "Light"
Most English Bitters are in fact IPA ~ Heavy is a darker and more flavoursome beer ~ not to everyone's taste. If you have ever tried one of those Guest ales known as "Winter Warmers" in your local ~ that is more like "Heavy".
But as you are a wine drinker don't let it bother you. The Scots really are most hospitable ~ just different.