I have 2 drives on Ubuntu. Can I use them together simultaneously?

Yes, you can. You have to be administrator, i.e., have sudo permissions, in order to manage storage media. Drive management and ownership requires some reading up. This cannot be covered in an answer here. so what follows are just some leads to get you started.

On Ubuntu, partitions are not automatically mounted after startup, unless they specifically have been configured to do so. On a default install, only the partition containing the system, i.e., the root partition, is mounted. It is mounted on the directory '/', the upper topmost folder in a linux system.

On Ubuntu, other partitions can be mounted before use by clicking the icon representing the partition in the left pane of the file manager Files. These partitions are then mounted by the system under a folder /media/<userlogin>/<label>.

It can be desired to also have data partition automatically mounted during startup. Power users can edit the system configuration file /etc/fstab directly, but you can also use the utility "Disks" to configure a partition to automatically mount. In that tool, select the partition in the map, then click the cog wheel and select "Edit mount options". You must specify a mount point, i.e., a folder in which the entire partition will appear after mounting.

Next to the aspect of connecting a partition to your file system (mounting), there is also the issue of ownerships and permissions. By default, a user can only read and write in folders under his home folder (typical /home/<login-name>). Before users can write anywhere else, either they must be made owner of the folder, or they must belong to a group that has write permissions for the folder. Alternatively, the permissions for others must be fully opened, but that is not safe practice.

A 120 SSD is plenty, both for the operating system and for storing user data that you use daily. In your case, I would work mostly from the SSD, and use the HD for storing archive data or large files like pictures and music. An elaborate scenario of a user arranging data in different partitions, and using links to make them accessible directly in the home folder is available here.