Few Problems need addressing with your help

Right I picked up a 98 a3 in September and in the past few months I've overcome a few problems. Hopefully with peoples help I can sort these out

Problem 1- on cold start it cuts out a fair few times and idles poorly, once warm the problem doesn't occur

Problem 2- when I turn the s/wheel if I'm turning/parking ect it makes a loud thud sound around the suspension area. Top mounts perhaps?

Problem 3- the sunroof motor works but the person I bought it from said the cog has broken. Can I get a cog? It has no numbers on it.

Many thanks. Lee