I think you're facing a drive formatting issue on your drive. Apple migrated from HFS to HFS+ with the release of Leopard. Snow Leopard if I remember correctly, is the last release that supported the older HFS formatted drives. So basically your stuck in a time warp!
Reference: Apple File System
To get your self out of this you'll first want to make a good backup of your data onto a HFS+ formatted drive. You did say you are running out of space on this drive, right ;-} This is a good time to setup a good backup system not only for your older system but for your new system as well!
The easiest way is to get a network attached storage system (NAS). Here you'll connect your systems to it using Ethernet then using TimeMachine to backup your systems. For your external drive you can just copy it over from your older system to a shared folder on the NAS.
Reference: Best NAS for Mac – for Households and SMBs
I would recommend setting up the NAS in mirror mode so each drive is a copy of the other in case one fails you have a backup of the backup files. Keep in mind the size of the unit is then half'ed so a 2TB unit is really just 1TB in storage space! I have a Drobo NAS and all of my systems use it for backup. Your needs will likely be less than mine. A WD MyCloud will likely serve you.