f(a)<=O(x): It means for function f(a) upper value cant go beyond x, so max value this function can attain is x.(not quoting from any textbooks just in simple terms i briefed it)
And as far as we are concerned we need to give closest upper bound as we can write many upper bound for above given expression.
exp1+exp2+......+exp N=exp always take max (exp1,exp2+...exp N) in calculating upper bound if like this is the given qsn and write every exp as max of the given, if for example exp1 is max than exp1+exp1+exp1+.....exp1(ntimes) this way you will give nearest and closest to upper bound for given expression.
Now coming to your qsn why ,
O(n-1)+O(n)=O(n) , we need to give upperbound for this expression ,as we can see max value it can attain is n, let see how
for O(n-1) we can write its upper bound as O(n) and for exp2 its already said max it can has is O(n).
so, you can write it as O(n)+O(n)=O(2n)=O(n) as we know O(c.n)=O(n)
Similarly, O(n/2)=O(n) and whole expression can be written as O(n)+O(n)=O(n)
now for your better understanding, we can rewrite above given exprsn as O(n)+O(n-1)+O(n-2)+O(n-3)+O(n-4)+...........+O(1) to find its upper bound you can again rewrite as O(n)+O(n)+O(n)+O(n)......+O(n)(n times)=O(n*n)=O(n^2)