1) My question is, how we know that the kernel of the atom of U-238, will absorb 1 and only, thermic neutron? I mean durring the fission of U-235, many neutrons are produced. How we are sure that only 1 neutron will be absorbed and not 2 or 3 or etc. Why it becomes Pu-239 only and not pu-240 or -241?
You don't/aren't. In general, the 2-3 neutrons will interact with different nuclei. At first, (starting from pure U-238), all the neutrons will find U-238 and make only Pu-239. Later, as Pu-239 builds up, this will sometimes absorb neutrons and Pu-240 and Pu-241 are formed. The bigger the neutron flux, the more Pu-239 is made, and the more higher Pu isotopes are made. The other Pu isotopes are difficult to handle. When Pu was made for weapons, the neutron irradiation is stopped when around 7-10% of the Pu is Pu-240, to keep this problem manageable.
2) If we have ONLY U-238 and not U-235, can we do U-238 --> Pu-239? How? (Can we use a mixture of Be/Po or something else?)
You can do this to a very small extent, but you don't make enough neutrons to make a large amount of material.
Consider the Pu-239 you'd need for a bomb, for an example. You need around 10 moles or so, at the very least. (2.5 kg) Now, say you have 1 kg of pure Ra-226. This is a
HUGE amount of this stuff and would be extremely difficult to handle. This much Ra is 1000 curies (by definition!) and thus emits 3.7E+13 alphas per second. If ALL of these turn into neutrons from reaction with Be, and ALL of these are absorbed by U-238, then you'd be creating 3.7E+13 Pu atoms per second. But you need 6E+24 atoms, and this is going to take about 5000 years. Worse, you don't get a neutron per Ra alpha. I have one source that says that you get 1.2E-4 neutrons per alpha, so with your 1 kg of Ra (which is totally impractically large), you now need to wait about 42 million years.
You almost certainly get less than one Pu atom per neutron generated, so 42 million years is still overly optimistic.
So, such a Ra/Be neutron emitter might make you microscopically small amounts of some material, but there is no way to get a macroscopic amount in any reasonable time. To get macroscopic amounts, you need a much, much, much larger neutron flux that you'd get with the Ra/Be source, namely a nuclear reactor.
EDIT: The times I first calculated were too big by a factor of 10, so it will only take you 42 million years, not 420.