Picaxe has two functions, either of which can be used to measure the speed of the fan..
Look up “Count” and ”Pulsin” in section 2 of the manuals. You will quickly see that both of these operate extremely fast, and neither require the complexity of including a clock.
Then you need some maths to convert the output of your chosen function to rpm. Look at the early section of section 2 on Picaxe maths. It has some wrinkles, but it will,get there.
Finally you need convey the answer to your 7 segment display.
Your Hall effect sensor will make an adequate speed sensor. They are really fast, even used to time ignition pulses in IC engines, but 50 rpm is really really slow for a Picaxe. I believe you will need more pulses from each revolution, or Picaxe just gives up and assumes the device is stopped before the next pulse arrives. However, a magnet on each blade might just work, and will give more options to make sure the fan stays balanced. Attaching the magnets will be your biggest challenge. You will really need more than ten and preferably a hundred pulses for a measurement of any accuracy so you will have to include some form of rolling averaging to get any accuracy from the number of pulses Picaxe can count before getting bored.
You will get plenty of help here with the maths side of the programme. It is simple enough, but the integer maths limitations make it a bit tricky at first. Have a go, then ask a more specific question. Use the simulation to see the answers you are getting.
Initially, for the display, just use your computer and learn to use “sertxd” with the programming jack still connected until you are happy with the results.
I have covered the path for the easy bits. Others will have to help with displaying the speed on 7 segment displays. I have not tried that yet, and have not got my head around the procedure. There have been recent threads that will help if you search back using the search function.
By the way, to give you an idea of the speed capability of Picaxe, try the little example program in the manual for “count“ to count how many times a switch bounces before it finally makes contact. You will be amazed at the result. And you will suddenly understand switch de-bouncing.
Eng460