When you select remove button on an entry in this table what does this do? If you make a mistake how can you undo it?

It will revoke that DHCP Lease. So when the client notices it's lease has been revoked the client will send a new DHCP-Request and the server will respond with a new DHCP-offer, and so the problem is resolved.

Another cool feature...
Before Mikrotik gives out the next IP, it'll check to see if that IP is being used on the network. If so, a lease is created where the mac is 00:00:00:00:00 and Mikrotik moves onto the next IP to give out.

How do you define "ip is being used"?

When an ARP entry is present in the ARP-table, one can surely assume that a given IP address is being used.

I'm not an expert on this, but @mkx educated me on this the other day. According to RFC2131 https://tools.ietf.org/html/rfc2131 Both server and recieving client should check the allocated address is not already in use.

As a consistency check, the allocating server SHOULD probe the reused address before allocating the address, e.g., with an ICMP echo request, and the client SHOULD probe the newly received address, e.g., with ARP.