- in the case of electrochemical cells/Galvanic cells: Oxidation at the anode (the A and O of electrochemistry, german people will know what I mean), reduction at the cathode (in electrolysis its the other way round)
- $EMF = E_{red} - E_{ox} = E_{cat} - E_{an} > 0$ for the reaction to run without external voltage (<0 in the case of electrolysis) "the higher redox potential always oxidizes the lower one"
In your case this means running the cell without applying any voltage gives an $EMF = 1.33 - -0.25 V = 1.58 V$
reduction at cathode:
Cr$_2$O$_7^{2-}$$_{(aq)}$ + 14 H$^+$$_{(aq)}$ + 6 e$^-$ $\rightarrow$ 2Cr$^{3+}$$_{(aq)}$ + 7 H$_2$0$_{(l)}$
(in the electrolyte -6e charges)
oxidation at anode:
3 Ni$_s$ $\rightarrow$ 3 Ni$^{2+}_{(aq)}$+ 6e$^-$
(in the electrolyte +6e charges)
(already multiplied by 3 for the total reaction)
total:
Cr$_2$O$_7^{2-}$$_{(aq)}$ + 14 H$^+$$_{(aq)}$ + 3 Ni$_s$ $\rightarrow$ 2Cr$^{3+}$$_{(aq)}$ + 7 H$_2$0$_{(l)}$ + 3 Ni$^{2+}_{(aq)}$
Now there is however a clear symbol in the electric cycle standing for a voltage source "V". This is indeed confusing and I would ask what was the meaning of that if the figure was actually titled "Galvanic Cell" which is the other way round. So if it would't be for the title and we would consider running the cell with external voltage, this would then turn around all reactions which I wrote before.
Other things that might be relevant:
- K$_2$SO$_4$ is responsible for the charge transfer between the cells. Since one cell produces positive charges in solution and the other one negative ones the electrolyte has to establish that the overall charge in both cells stays neutral. The salt bridge connects the electric cycle, without it, the cell won't run for long
- the Gibb's energy is related to the EMF. $\Delta G = -n\cdot F\cdot EMF$, so again a positive $EMF$ gives a negative $\Delta G$ which means the reaction runs "alone" without external voltage, the Gibb's energy provides the driving force. n is the number of electrons involved in the redox reaction (6) (F is the Faraday constant, a natural constant)