Now, if you'd gone with a radiator from Complete Radiators you wouldn't have a "strange
" entry pipe!
But, no, do
not cut that, as you have it is fine.
I've never "bled" teh radiator as such, but do follow the precess outlined in the manual:
Fill the radiator to the base of the filler neck and add coolant to the expansion tank up to the "Full Hot" mark. Fit the expansion tank cap, but
not the radiator cap.
Start the engine and run it until it reaches normal temperature (the level in the rad will almost certainly drop away soon after the engine is started - I sometimes add a little), and, while it is warming I do give the top hose the occasional squeeze, just to get the water "moving along".
When the engine reaches normal operating temperature, and with it idling, add coolant up to the base of the filler neck and replace the radiator cap. (Use a funnel, the fan blows water everywhere!)
If any further adding of coolant is required (normal topping up) this should be added to the expansion tank, ideally when the engine is cool and to the Full Cold mark.