If you had problems with the hard drive is the drive even healthy? If the hard drive is healthy, then I'm surprised the tech didn't setup a Fusion Drive for you so you wouldn't have this problem. I personally don't recommend custom setups as you are suggesting because it is so easy to break something even if you know what you are doing. If you are able to backup all your stuff to an external drive, then I would suggest creating a Fusion Drive by combining the SSD & HD so you get the speed of an SSD and the storage space of the hard drive. Here are the instructions to create a Fusion Drive. Just make sure to create a bootable macOS USB installer first and verify it will boot your system before trying to create a Fusion Drive.
In answer to your question, it would be possible to do what you want, but I'm not the one to instruct you. If you are that low on space, then I'm not sure moving the Applications will free up enough space for you. It would be better to have your home folder on the hard drive so all the large files from photos, videos, music, etc. are stored on the larger hard drive, but then they would be on a slower drive. Personally I suggest you look into setting up the Fusion Drive.
Make sure to clear out your Downloads folder and empty the Trash to free up space. Rebooting your computer will also help remove some temp & cache files which might be building up on your system.
I'm not a fan of installing an SSD into the optical drive bay of a Mac since the SATA controllers for the optical drives do not always work well with an SSD. The reliability varies greatly depending on the exact computer model.
What size SSD was installed? SSDs are relatively inexpensive today and it is fairly affordable to use a 1TB or 2TB SSD which is a much better option than using a slow hard drive even in a Fusion Drive setup especially in an iMac where the drives are hard to access and replace. If you need more than 2TB of storage, then using an external Thunderbolt or USB3.1 drive would be a good option to store your large files.