Identify these potentiometers or variable capacitors

They're IF transformers (T is for Transformer) used in radios (relatively narrowband amplifiers at the Intermediate Frequency of usually 10.7MHz for FM and 455kHz for AM).

The ferrite core adjustment is for trimming the inductance to tune the center frequency, called "aligning" the radio. Below image from this datasheet.

There are many variations and you need some equipment to properly align a radio, which does not bode well for your chances at success.

They are variable inductors, used for fine-tuning frequencies.

These are variable inductors used for trimming specific frequencies. Usually, you also need an oscilloscope for repairing and re-aligning these old receivers. Here's a YouTube channel that specialises in doing exactly that: MrCarlsonsLab

Alternatively, you could measure every component in the circuit with a precise multimeter and figure out what value you're supposed to set these at by understanding what particular frequency the component arrangements are filtering out. Here are some online calculators for simple frequency filters:

https://electronicbase.net/band-stop-filter-calculator/

http://sim.okawa-denshi.jp/en/Fkeisan.htm