Free Spirit "Brittany Te12" Part Identification/Upgrade
tl;dr: knowing the parts is useless. You have a caliper, now you just need to remove everything and measure everything. You will learn something just by disassembling this bicycle and not focusing on brands, just on dimensions and &quot;mechanics&quot; of the parts you are removing.
Then, about reassembling it, it will cost you 5 times the money and 50 times the time+effort with respect to a bicycle shop.
Disclaimer: I do not own a bicycle shop.

The parts currently installed have no value and will provide very little information on their own.
You can still disassemble them and try to understand a thing or two on how they are assembled and maybe how they work, especially about the derailleur (springs, limiting screws and so on).
Bottom bracket and cranks are good to be recycled (=scrap metal), as well as the chain and whatever is installed on the rear wheel as a cassette.
New bottom bracket and crank ---&gt; most likely new chain line. Which is not that bad considering that the wheels will almost for sure need a good clean (greasing the hubs and so on) and you may discover that they are in bad conditions, so counting them temporarily as scrap metal as well, the new chain line is less of an issue (you have a lot of freedom once you have to replace bottom bracket, crank, rear wheel).
So remove the bottom bracket, check whatever size is relevant.
Then check the fork. Remove it, give it a thorough clean and a good examination, check for cracks in the fork or for deep rust. You do not want a fork that breaks in half while sprinting across an intersection, nor while you are just coming up/down from the curbs.
Check and note wheels size.
Save the frame, maybe the fork, then you have a lot of freedom in how to reassemble this bicycle.
I forecast something on the order of at least 3/400 USD/EUR/GBP, only for the parts (assuming you have all the needed tools for cassette, bottom bracket, fork, etcetc).