Graham, in the first picture the current engine looks like it might be a Honda (because it has a red cowl). It is important to work out whether the mower was made surprisingly recently and that engine is the original one, or the machine is from the 1950s and originally had some ancient British engine. This is important, because the mountings and crankshaft height are likely to be different. Was it made originally with a modern (Honda) engine, or has it been converted? Also I take it that the engine is defunct, or you do not want to rebuild it? Essentially, there are three ways you could go:
Option 1: restore the mower to its original specification, whatever that was. By doing that you make your machine into a potentially valuable collector's piece.
Option 2: repair the mower at minimum cost. That would involve identifying the current engine and then finding a second-hand four stroke engine that is physically interchangeable and has at least as much power.
Option 3: fit a new engine. You would still need to establish what type of engine fits the machine, then buy a reputable engine that is physically interchangeable. It would need to be a 4 stroke to suit the kind of service it will be used for. Between them, Briggs and Stratton and Honda produce the bulk of the world's engines of that general type, and both make excellent engines, subject to some quality control questions in the case of Chinese-made versions of both brands.
So, the first thing you need to do, is decide what you are trying to achieve: just mow the lawn, or acquire a classic mower and preserve it for posterity. The best classic mowers are restored to their original configurations, so you would need to find out its exact specification when new, then make a plan to return it to that condition. Before you go too far with plans, you need to verify the condition of the parts that would be difficult to restore if they are badly damaged. Examples are the drive cover, which presumably has to end up oil-tight, and the gear train inside it. If bad things have happened in there, the Scotty 45 will start to look like a really good option.
With regard to the roller, cast iron is usually regarded as quite weldable unless it is "white" cast iron (i.e. chilled during casting, to make it hard). However to end up with a good quality, robust, cylindrical outside surface is quite a lot of work.
