Running Time for Finding Maximum
Question 1

I think you are overcomplicating things, the question is about $\mathcal{O}$-notation, you don't need any meaning attached to these constants. Try making your life easy and pick simple ones:

You only need a lower bound, so just set $c_1 = d_1 = 1$, clearly $n + 1 \leq T_{\text{findMax}(n)}$.

Similarly you only need an upper bound, set $c_2 = 4$ and $d_2 = 42$, giving you $4n + 42 \geq T_{\text{findMax}(n)}$.

Question 2

It's not clear how $T_A$ is defined, so it's hard to answer Question 2.

Assume there is an algorithm $A$ with $T_{A(n)} = t &lt; n$. So this algorithm is restricted to read/compare at most $t$ elements of $a_1,\dots,a_n$ and therefore there is always a sequence $a_1,\dots,a_n$ where the algorithm will fail, ie. the actual maximum is not among the $t$ elements. $\Rightarrow\!\Leftarrow$