4500 line cards are hot swapable, so the answer to the first three questions is yes (assuming a 45xxR chassis).
A couple of caveats, for question 2, the supervisor has to meet the requirements for redundany. For instance, you would not be able to insert a Sup7 in a chassis with a SupIV. Additional configuration may be required as well to enable the redundancy properly.
For question 3, you shouldn't remove an active supervisor (while you can, this isn't best practice). If the supervisor you wish to remove is currently active, failover to the standby supervisor first.
The answer to the last question is yes, you can cause damage to the chassis and/or line card if you insert them incorretly (i.e. this has nothing to do with the chassis being running, but a purely mechanical problem). The levers should be open when inserted, the card should glide in easily until the levers start to close by themselves, and the final insertion should be done with the levers. If you have to use A LOT of force, it may not be aligned properly and you could result in damage.
On the 4500s, you also need to make sure you are using the proper slots. Do not try to install a supervisor module in a linecard slot or vice versa.
Fixed! Turns out, after slagging off the netgear, it was the cisco that was causing the problem. Seems when I configured the interface switchport access vlan 20 it didn't create vlan 20 on the switch automatically like it would normally.
Found it by doing a sh trunkand VLAN 20 wasn't included in any of the trunks, did a sh vlan and it wasn't listed either, so created it and all working. Very odd.
Best Answer
My knee jerk reaction to this would be to say "don't do it." Mainly because these switches would not support data center bridging. FCoE is not like iSCSI. FC is a bus and assumes it is lossless. Ethernet, as you know, is lossy. DCB allows Ethernet to act lossless and transport FCoE frames.