"Experimentally" means "by means of experiments". You need to devise a method of performing experiments and measuring experimental data, then analysing the data to get the answers you want (rate constant and activation energy). Obviously you don't need to give specific experimental details e.g. quantities of chemicals, solvent, temperature, rate of stirring etc. because it is an idealised reaction and we don't know these specifics. But you need to say what experiments you would do, what data you would measure, and how you would analyse the data. Thus;
(i) Perform the reaction (obvious!). But how many times? You have to do more than 1 experiment to get the results you need. What parameter(s) would you vary between reactions, and what would you keep constant? (Note: I assume "temperature is held constant" means constant during an experiment, but T can be varied between experiments.)
(ii) You are told "concentration of A can be measured through spectroscopy", which is a strong hint that you should measure [A]. When? beginning? end? during reaction? once? often?
(iii) What do you do with the [A] data? What graph(s) do you plot, and how do you extract the required quantities from them. If you know any formulae/equations for first order reactions (and I hope you do!), they can tell you what data you need to obtain the required answers.