Hi,
No idea about the plastic stopper on the original, with Pattern parts they often do away with bits that are not actually used, even so OEM parts are not always truly identical as I found out when I fitted a new main radiator, had to do a bit of adjustment to the mounting brackets as the main part of the core was a larger - probable reason, the part is used in many other different vehicles.
Yes, ours is the Climate control version or as the Toyota button says AUTO.
Your first post / link to the part you say you ordered gives part no MRH0740 yet the link above in your last post above is MRH0915 , which says for the 1.8 TS,, so which one have you actually got ?
Again do not have any idea of what kind of clamp /fitting is used on those Ends , but would assume even with a rubber seal it should feel properly firm as its bound to be affected by the heat / pressure.
Think you are better speaking to the supplier if in any doubt, after all they should know their products , better safe than sorry !