Is it possible to backup the message (e.g. SMS) and contacts inside my SIM card to my external SD Card without transferring them into my Android phone?
That should be possible. There are plenty of backup apps available on Google Play which allow local backups, such as SMS Backup & Restore or SMS Backup. For contacts, there's e.g. Contacts Backup, and for both together Super Backup : SMS & Contacts. They all store the backed-up data e.g. on your SDCard.
Though I found no explicit mention of SIM messages, I'd assume they are covered – but you might wish to check for yourself to make sure.
Update: As it turned out, above apps do not seem to cover SIM storage. But I've just stumbled upon Backup2CSV, which explicitly lists to Export contact directories (SIM CARD and phone) (it also lists Export text messages (SMS), but does not explicitly mention the SIM card in that context).
You can use the G Cloud Backup to backup you SMS, Contacts, Call Log, Photos and more to a secure cloud servers.