How to properly use STM32 flash memory as an EEPROM?

Yes, as you've already discovered, you can't erase less than one page at a time.
However, if your parameters take up much less than the size of a page, you could consider creating a scheme where instead of writing to the same address every time and erasing in between each write, you write to a different address within the page at each write. Only erase the page when its full.
So when you want to read your parameters, start reading at the beginning of the page, and continue reading until you get to a parameter bock full of 0xff entries. You'll then know that the previous block was the last one you wrote.

There are certainly many other ways to do this kind of thing, for example you could use a bit-field at the start of the page to indicate which blocks within the page have been written instead of having to potentially scan through the whole page. But this may depend on hardware support. Some micros - like the STM32L0, won't let you write anything other than 0x0000 to a flash location if it's not currently fully erased to 0xffff, preventing you from using it as a bit- field and clearing 1 bit at a time.

Yes, an entire page must be erased (set to 0xFF) before you can start writing to it.

With most external flash memories, you can actually write to a page multiple times without erasing as long as you are writing to previously-unused byte locations. Please see this answer.

However, the internal flash memory controller in the STM32's won't allow any writes unless the entire page is cleared.

If you want to go the easy route, ST has a freely-available software solution which provides an EEPROM emulation layer using an area of internal flash memory. It provides a simple set of functions, and handles all the complexities "under the hood". It allows for single-byte read and write granularity, and handles the erasing for you.

I don't know which microcontroller you are using. Here are the EEPROM-emulation docs for the STM32F0xx and STM32F10x microcontrollers.

For example, you write a byte using EE_WriteVariable(). The software maps this location to a flash page, reads that page, inserts your byte where appropriate, then programs an entire new page onto another flash page. It bounces back and forth between pages, and keeps all this hidden from you.

However, this is pretty time-intensive. Not only does it take a while, but your memory bus can stall while waiting for a flash write to complete, so you can't do this on timing-critical applications.

If this software doesn't work for your application, you can build up as complex a solution as you need. Once I wrote a large system for handling mission-critical configuration data, which data could change on the fly. It used multiple sectors, redundant locations, crc-verification, wear-leveling, etc. I couldn't rely on a table-of-contents, because what if the system powered down in the middle of the TOC update? So it had a routine to discover the "active" (read: "most-recently-written") flash configuration bank upon initialization... etc etc.