When redistributed from one process to another they would appear as normal E2 routes (unless configured to be E1) so you are correct that you can redistribute from process 1 to process 2 and then process 2 to process 3.
I would definitely like to see the network topology that needs 3 ospf processes though.
"I have a router with 3 ospf processes, can I redistribute ospf 1 into ospf 2, then ospf 2 into ospf 3 and expect to see routes from ospf 1 redistributed into 3?"
The answer is no. All redistribution between protocols happens via the routing table. In your example, if a route is learned via OSPF 1 and installed in the RIB, it can then be redistributed into OSPF 2. For the second part redistributing OSPF 2 into OSPF 3, the route will not be found in the RIB as an OSPF 2 route and would thus not be redistributed into OSPF 3.
"Or will I have to directly redistribute ospf 1 into ospf 3 aswell to see ospf 1 routes in ospf 3?"
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