Calculation of size of screw

Shear strength of material used for screw x min number of threads in use x 3.14 x thread mean dia x width of one thread at mean dia,= 25 T

Either you design a suitable thread or look at a 'screw jack' of 25 ton capacity and take the dimention of the screw of that...

Go for ACME or Tr Thread rather than the usual metric/ UN threads.

It is not just the size of the screw to be concerned with, you also have to consider the grade. As an example, a 1-8 bolt in a grade 2 has a total tensile strength of around 33,000 lbs., but in a grade 9, it is around 93,000 lbs. (no safety factor included).

How much of safety factor you want can be influenced by the application. Does failure present a threat of injury or death? Is it a high cycle application or used only a few times a week?

As a rule of thumb, a bolt should be threaded to a depth of at least 1-1/2 times the diameter to reach a tensile strength of the threads that is greater than the tensile strength of the bolt head.

Threading the bolt only part way in where no torque can be applied though tightening is generally not a good idea. The play in the threads can result in an "impact" type of force much greater than a basic tensile force. Any shear forces that are applied will be directed entirely on the bolt rather than being absorbed by the friction between two parts that are firmly bolted together.

Paragraph #1 and #2 are general guides but the task has been adequately defined.

As for paragraph #3 and #4

For standard bolts, paragraphs 3 & 4 are not BS. If he designs a custom thread or uses acme specs as previously mentioned, it will be different. Mild steel frame and force are not enough to define the design of the press and if he has to ask about screw size, then you should be asking more about design. Perhaps in the future you could present a more positive response than just posting a cute little picture.