Looking at that, I suspect the cast pipe was simply placed into the clay socket, a piece of sacking or similar wrapped around to prevent debris getting into the drain, and the joint sealed with mortar. It's doubtful that joint will come apart without breaking something, (clay probably), so you would be best cutting the clay at a convenient point, and redoing that section. Modern jointing methods will allow some flexibility, so going forward, any movement should be accommodated. (Going to be pedantic, but should point out, that old drain is 'Salt Glazed Stoneware', the new clay drainage is Vitrified Clay.)
Unlikely a silt trap was ever fitted on that, a direct connection was made to the drain, which would lead to a soakaway. Any rainwater connection to a combined sewer in that era would have been via a trapped gulley. The presence of soil pipes nearby is probably unconnected, the drains would have been laid as required to suit the building layout, and rainwater and foul drains passing over/under each other where required.
Dye testing can help trace drain runs, but only if the dye can be seen downstream. Given it seems likely these rainwater pipes are heading for a soakaway, dye testing would probably be a waste of time, so it leaves sonar tracing, (expensive), or a bit of old fashioned digging. Provided you only clear the soil from above the pipes, there shouldn't be an issue, you only need to ascertain the route, not the condition.
I'd get a 9" angle grinder for cutting the clay pipes, anything smaller will struggle, (bear in mind the pipe wall is at least 1/2" thick), and then swapping the stone disc for a metal disc, should allow you to cut the cast above the socket if it aspires the cast has been joined with run lead. Not sure what you mean by 'high priced silt scoop grabs', but
Wickes do a wet vac for about £45 which is ideal for cleaning out gullies!