What is the difference between these two Feynman diagrams? In which direction is time flowing and what reactions do they represent?

EDIT for Gigi (I could not add a comment to your answer):
1) Do Feynman diagrams by definition only show fundamental particles?
2) why does the second diagram show how neutrons transform into protons? In which direction is time flowing?
 A: Your two diagrams are equivalent.  Let's discuss the top version.
Suppose time flows from bottom to top.  Then the diagram shows a proton absorbing an antineutrino, changing into a neutron and an antielectron.  This was the reaction used in the antineutrino discovery experiment by Reines and Cowan.
Equivalently, you can say that the antineutrino is moving backwards in time, in which case the top diagram shows $\beta^+$ decay.  Sometimes in that case the author of the diagram will draw a fat line parallel to the neutron-proton line, to indicate that there are more spectators happening in the nucleus.  It depends on the context.
Suppose instead that time flows from top to bottom.  Similarly, this could show neutron $\beta^-$ decay (though it'd be unusual to draw a time-reversed antielectron and a time-forward antineutrino).  It is also the diagram for weak positron capture on the neutron, even though that's not a reaction that could ever be observed using ordinary matter — a slow positron would annihilate on an electron first.
Now suppose that time flows from left to right.  Based on the directions of the arrows, your diagram would show an antineutron and proton annihilating, weakly, to produce a positron and neutrino.  Like the positron-neutron interpretation, this is a little silly: a baryon-antibaryon annihilation will prefer to proceed by the strong interaction, and make a boatload of pions.
This is a strength of Feynman diagrams: the matrix elements for all of these interpretations is the same, so you can interpret the same diagram multiple ways.
When I see diagrams like this, I expect the accompanying text to discuss $\beta^+$ decay or antineutrino scattering.
A: Explanation of event:
Both diagrams show same event proton $p$ and anti-electronneutrino $\bar\nu_e$ collision. It happens due to Weak interaction: proton decays into neutron by absorption of anti-electronneutrino and it gives positron $e^+$ because of emiting $W^+$ boson (it acts as an 'exchange particle'), this reaction can also be represented in this way: $p+\bar\nu_e\rightarrow n+e^+$
What is Weak Interaction? (Examples):
this Diagram shows how protons transform to neutrons:

this reaction can also be represented in this way: $p\rightarrow n + \nu_e + e^+$
this Diagram shows how neutrons transform to protons

this diagram can also be represented in this way: $n\rightarrow p + \bar\nu_e + e^-$
So in first diagram(in my answer) protons transform to neutrons, We all know that protons and neutrons aren't fundamental particles, and they are made of smaller particles called Quarks, proton is made of two up quarks and 1 down quark, and neutron is made of two down quarks and one up quark, so in diagram you can see how up quark transforms into down quark (while two other quarks remain unchanged) by emiting $W^+$ Boson which decays to $\nu_e$(electron neutrino) and $e^+$(positron). They you will have a question: how can up quark decay into $W^+$ boson which is many times heavier that proton itself, it is because of Quantum Mechanics, at that scale there is high uncertainty in energy in other words you can 'borrow' from vacuum any amount on energy for short amount of time, equation that describes this is often written like this:
$$
\Delta E \Delta t < \hbar
$$
Second diagram(in my answer) shows how neutrons transform to protons, in other words two quarks (one up quark and one down quark) stays the same and one down quark transforms to up quark by emiting $W^-$ boson which soon decays into anti electron neutrino and electron.
this diagram shows proton $p$ and electron $e^-$ interaction:

this diagram shows how proton $p$ interacts with electron $e^-$, proton decays into neutron because of absorption electron $e^-$ and produces anti-electroneutrino by emiting $W^+$ boson. this reaction can also be represented in this way: $p+e^-\rightarrow n+\bar\nu_e$
and this diagram shows proton $p$ and anti-electroneutrino $\bar\nu_e$ interaction (which I have explained in the beginning of this answer)

Conclusion: 
Both of your diagrams show same event.
A: As this is homework, the answers are supposed to guide you into thinking for yourself.
Feynman diagrams are read any logical  way, if the lines represent elementary particles.

First of all one must choose the lines that comes first in time, the incoming particles.
In this simple example, if one takes the time axis as the y axis for the two incoming ones, one reads it as two positrons ( particles pointing the  wrong way to the vertex are antiparticles ) scattering with the exchange of a virtual photon into again e+ e+ scattering. If you take the -y axis direction it is e-e- scattering. 
If one chooses the x axis as the time direction for the incoming then in this simple example we have e+e- scattering into e+ e-  through a virtual photon.
So one chooses the time direction and plots the reaction. You should look at your diagrams in the logical sense for the experiment: what is it that you want to calculate.
Your diagrams are weak interaction diagrams and since they involve the proton and neutron they must have something to do with neutron decay or with antineutrino proton scattering.
