Do I lose RAID array if I switch RAID controller

The removed drives still have the RAID metadata on them. When you went to step #3 in the first drive replacement process; Boot up the server and acknowledge errors about failed drives, did you DELETE the removed array/logical drive or just mark it as failed? That's probably the source of the problem here.

When you brought up the system with your old drives, you should have again deleted the new data logical drive either in the BIOS raid utility or with the Smartstart/DL180 Setup Array Configuration utility and let the controller detect the array/logical drive.

Try this. Boot up with the new drives removed. Go into the BIOS or DL180 setup disk Array Config and delete the RAID 1+0 array. Then boot with your old drives and see if they're detected. Get the data you need. Remove the old drives. Delete the array. Insert your new drives. Let the controller discover the new array. Restore your data...

Keep this HP Smart Array controller users guide handy. http://h20564.www2.hpe.com/hpsc/doc/public/display?docId=c01608507

PERC 6i is LSI gear, so in general anything that goes with the MegaRAID SAS controllers, will work on the Dell PERC.

We can add a disk to the array one at a time, and the controller will expand the array

You will notice this not to be the case. Just adding the drives will make them available for the use in a new container, but not automatically grow anything. You should be able to use the Dell OpenManage tools to add the disk to the array as a replacement for a defective or offlined disk - the array will regenerate by writing redundant data to that disk.

What we do not know is what happens when ALL the drives have been replaced, and are now 450Gb drives, does the RAID controller automatically grow the array to use all 450Gb on each of the disks or will we end up with 50Gb wasted space on each drive?

At first, it is the latter - your array will be the same size with unused space on each of its disks. But you might try to expand your virtual disk using OpenManage Storage Manager. Please note that the expansion of the virtual disk will not expand your partitions and filesystems contained there. You will need additional software to do that - a GParted live CD should cope with most resizing needs and will support your controller out-of-the-box.

will the controller allow us to then create a new RAID 5 array using these 6 x 50Gb spaces

Yes, but you should only do this if the disk expansion is infeasible for some reason.

With all that said, it is a complex operation which might fail and take all data with it at any stage, so having a backup which can be restored swiftly (e.g. a full disk image) is strongly advisable.