equilibrium, optimum, and decentralizing the optimum
Q1 Optimal usually means one of two things:


Pareto optimal (there's no way to change the outcome such that everyone is at least as well-off, but someone is strictly better-off).
Optimal in the utilitarian sense (we maximise the sum of everyone's profit/utility).


If utility/profit is quasilinear then the two concepts coincide.

This paper appears to be using the utilitarian standard: the optimum is the allocation that minimises the sum of everyone's costs (which, in this case, are the time spent travelling and parking).



Q2 To understand what is meant by decentralisation, it is useful to first know what we mean by centralisation. We say that a decision is centralised if there is one agent (often called a "social planner") who makes all of the decisions and imposes them on society. 

We know from experience that governments are not very good at centrally planning things (cf. the USSR). Thus, an interesting question is whether we can set up a market, system of prices, or other kind of mechanism such then we can leave each individual to his/her own devices and still end up with the optimal outcome (such as how we get the efficient outcome under perfect competition, without any kind of central planner).

When everyone is left to their own devices like this, the market is said to be decentralised. We say the optimum is decentralised if we find a way to decentralise the market such that the end result is optimal.