Washing up liquid is ok as long as you dont over use it in a mix , you only need a little bit , plus most things soap flakes shampoo hand cleaner anything frothy will do just dont over use it
builders merchants is the best bet for purchase , save on money , ask them as they will have a best seller the local builders buy , dont bother with DIY out lets to pricey
As long as you got the old bricks you should be able to match the brick work bond correctly above just use lime and cement plus sharp sand for the mixing , just remove one brick at a time and taking your time