şaloma's questions

My NIC supports gigabit ethernet:

$ ethtool eth0
Settings for eth0:
        Supported ports: [ MII ]
        Supported link modes:   10baseT/Half 10baseT/Full 
                                100baseT/Half 100baseT/Full 
                                1000baseT/Full 
        Supported pause frame use: No
        Supports auto-negotiation: Yes
        Advertised link modes:  10baseT/Half 10baseT/Full 
                                100baseT/Half 100baseT/Full 
                                1000baseT/Full 
        Advertised pause frame use: No
        Advertised auto-negotiation: Yes
        Speed: 100Mb/s
        Duplex: Full
        Port: MII
        PHYAD: 1
        Transceiver: external
        Auto-negotiation: on
        Supports Wake-on: g
        Wake-on: d
        Link detected: yes

My question in other words: I don't know the LAN I am connected to is whether a fast or gigabit ethernet. It could very well be gigabit ethernet and all that time I would have been using only 100 mbps instead of 1 gbps. But since I am connected to LAN with a CAT5e cable (I don't possess a CAT6 cable), is there any way to tell?

i am logging onto ssh server from my laptop and i have my private key there but i would like to logon also from my desktop at home, so how can i copy the key?

OS: ubuntu

Apparently someone on my LAN is running his own DHCP server (by mistake I assume) and broadcasting an address (yep it is 192.168.1.155) prevents me to connect to the 'real' DHCP server (195.249.186.1). how can i connect to my usual DHCP server? what commands should I use?

How can I issue a nmap command that shows me all the alive machines' IP addresses and corresponding hostname s in the LAN that I am connected? (if this can be done in another way/tool you surely are welcome to answer)