Building a pseudo-solenoid electromagnet - Heat disipation
Can I limit the current into the coil by placing a resistor before it?

Yes you can. A resistor in series with the coil will limit the maximum current taken by the coil.

If a given coil setup draws 1 A, and I limit that to 0.5 Amp, what
would be the ballpark impact on the magnetic force (1/2, 1/10,
1/1000)?

The attractive pull of an electromagnet are governed by several factors: -
Force = \$(N\cdot I)^2\cdot 4\pi 10^{-7}\cdot \dfrac{A}{2g^2}\$

F = Force
I = Current
N = Number of turns
g = Length of the gap between the solenoid and the magnetizable metal
A = Internal area of coils

If current, area and turns are constant, Force is inversely proportional to the gap squared (\$\ell^2\$). Formulas taken from this question.
So, if current is halved, the force on the magnetizable material quarters.

If I change the material of the tube from plastic to soft iron, will
it still generate a magnetic field inside it?

No it won't well, not to any great extent because the field lines will converge into the iron and that means virtually no field in the centre.

Would it be a bad practice to place a fan or two on the coil to keep
it cool?

It's up to you. I don't see it as bad practice.

Edit: The discussion in the comments has given me another question,
what if instead of coiling on the cylinder, I coil it inside and out
like in the picture below AND use an iron cylinder instead of plastic?

No it won't work because the magnetism will remain inside the iron core and not attract anything external to that core. In other words, electromagnets need an air gap.