No water coming out of outside tap

I would contact a qualified plumber

you really should get a qualified plumber to look at this for you.

Hi. I think the banging is probably un-related to the outside tap issue & has arisen or become noticeable since the washing machine has been connected to the cold main. It is likely to be due to a loose pipe clanking when the washing machine inlet valve opens & closes. Being a sudden on off action may be enough to jarr a pipe where more gradual closure of a tap doesn't or you are in an area of the house where it can't be heard. The lack of cold water in the outside tap is most likely due to a check valve being jammed, which is very likely that your tap has fitted. In fact they have 2. They can freeze during the winter & it's common for the 1 at the rear of the tap to have its O ring squeezed through to the other side of its seating which then prevents the check valve from opening. It is usually a very simple fix, by removing the tap & carefully pushing the exposed portion of the O ring back through & depressing the check valve to ensure that it opens. This is the most likely cause of the problem, if not then whilst the tap is removed, open the supply & see if you have water at the wall plate. If not then there may be a check valve on the inside which has jammed, but 99 times out of 100 it will be the rear check valve in the tap. I hope this helps.

Ensure all pipes are fixed securely. A shock arestor is another alternative to solving noisy pipes

It sounds that u got an airlock in ur system. If u have a combi then it should clear but if it is a system boiler with a tank in ur airing cupboard then it is quite difficult to get out. I would recommend that u get a professional to have a look. Hope this helps