Hello.

How can I check what mode my ethernet card is working on?
My datacenter says it is 1 Gbit and they show me MRTG graph of my bandwidth with about 10 Mb spikes (their MRTG takes an info from a router) but I have own mrtg installed at the server and it shows less then 1 Mb spikes. So I assume my ethernet card works as 10 Mbit card.

Are there some tests how I can prove that?

My server is running under RedHat Linux 7.3

Thank you.

you can try to perform a less /var/log/dmesg

mine logs this :
eth0: Setting 100mbps full-duplex based on auto-negotiated partner ability 45e1.

I checked dmesg early but it shows only type of the network adapter. My dmesg shows it is Intel® PRO/100 VE:
eth0: Intel Corp. 82801BD PRO/100 VE (LOM) Ethernet Controller

I assume PRO/100 it's 100 Mbit card.

It is a 100mbit card but it can operate at half duplex, check with ifconfig.
on FreeBSD it would look like:
media: Ethernet autoselect (10baseT/UTP)
or
media: Ethernet autoselect (100baseTX <full-duplex>)