The description of Free Actions on page 163 of the core rule book for 5th Edition covers your question, I believe. Essentially, this is a situational determination based on the description from the player, the sequence of events, and the GM's ruling. It's not set up in a comparative relationship like 2 Simple Actions = 1 Complex Action. Free Actions are an aspect of activity in an Action Phase that cover all the little things which could be occurring at the same time as the meatier actions.
In the question, a sequence of events is provided as an example. Where that sequence runs into some trouble is that it is a linear series of discrete actions. Free Actions are minor things (dropping something, saying a word) which require little to no attention to carry out and can be completed while the character is performing their Simple Actions or Complex Action.
Using a Simple Action to Take Cover and adding a Free Action after that to Drop Prone, but pausing to communicate in word and gesture before they Take Cover and somewhere along the way dropping what is in their hands is attempting to compress a lot of time into the Phase and focuses on one thing happening after the other. If the player can describe how it works, and the GM is fine with it, that is fine. The intention of the rules seems to be to not control and limit every aspect of character action, while also not leaving a large hole for abuse. As an example of this, if the character wants to run instead of walk, it burns a free action. Basically, characters have 1 free action. Only allowing one Free Action would mean to some reading the rules that you cannot run and drop something at the same time, hence the freedom to expand the amount of free actions to fit the shared view of the scene. What I think is a key point of all of this is that Free Actions are occurring as a part or as a compliment to the Simple or Complex Actions which the character is making in the scene, and occur more or less at the same time.
Were I to be asked to make a decision in this case because the outcome of the scene hinged on whether or not a character could do all of these things in one Action Phase, I would lean toward suggesting that the sequence could more easily be resolved by having the character dive for cover while dropping the object and shouting. This covers their two Simple Actions (Moving to Cover and Taking Cover), and does not require a lot of Free Actions: dropping an object while running, speaking a short phrase while running and taking cover. The two simple actions may occur more or less sequentially, and the Free Action(s) occur during one or both.
It's not so much trying to squeeze as much into one phase as possible, but trying to break down what is actually happening within a (3 second or so) frame of time.
Upgrading the Pilot program
The simplest solution is to increase your Pilot program, the drones on the core book were all limited to their factory Pilot program (rating 3 or 4), but Rigger 5.0 gave us some prices on more advanced Pilots (p.126). But keep in mind that drones equipped with rating 5-6 are generally military-grade (F) and might cause you some issues.
- Rating 4: 12R, 3,200 nuyen;
- Rating 5: 16F, 10,000 nuyen;
- Rating 6: 24F, 20,000 nuyen.
Using better weapons
Upgrading your weapons will also grant you a few benefits in combat, such as:
- Laser Sight (CRB p.432), 125 nuyen: This will increase the weapon's Accuracy by 1 point, and add +1 dice to your attack checks. But this is not cumulative with smartgun systems (more on this below);
- Improved range finder (accessory) (Run & Gun p.52), 2,000 nuyen: This will reduce the range modifiers (CRB p.175) by 1 point;
- Silencer/Suppressors (CRB p.432), 500 nuyen: This may sound weird, but if the enemy cannot detect where the bullets are coming from, they cannot effectively dodge them or even fire back at your drone (which is really important). Those will apply a -4 penalty on Perception checks to notice your drone. See Surprise (CRB p.194);
Characters who are surprised cannot take any actions that directly affect, impede, or counteract characters who are not surprised. This means surprised characters cannot attack the non-surprised characters, nor can they dodge or defend against attacks from those characters;
Firing modes
I know this is fairly obvious, but using semi-auto and full-auto firing modes will drastically increase the chances to hit a target, as you are effectively reducing their defense pool against your attacks.
- Burst or semi-auto burst: -2;
- Long burst or full-auto (as simple action): -5
- Full-auto (as complex action): -9
With this in mind, grab the heaviest weapon you can that is capable of full-auto as a complex action, and send the same firing command to all your drones. Not only they will have to reduce their initiative in order to gain a higher defense pool, but you might be able to completely negate their defense check by reducing their pool to 0 dice, which means automatic hits with a single success on your attack check.
Sensor targeting
When your drone is targeting, you have two options: Passive and Active targeting. The drone makes a Pilot + Clearsight [Sensor] check in order to find her target, applying a modifier based on the Signature Table (p.184) and check the results based on the type of sensor targeting being used:
- Passive: You replace the weapon's Accuracy by the drone's Sensor rating. This can help you if you decide to use a cheap weapon like the Colt M23 (Accuracy 4, Damage 9P, -2 AP, 550 nuyen) as most sensors can have up to rating 6. But this is not really why we are here...
- Active: Now, this is why we are here. This is a Simple action and will make your drone "lock-on" a target. The result of your sensor test will be used as a penalty on the target's defense check. This means that even if you are using the factory sensors (rating 3) and manage to get 3 successes on that check, the target will receive a -3 penalty on all their defense checks against your drone's attacks. The best part is that you don't need to make another sensor check unless the target manages to completely disappear from the drone's line of sight.
Also, keep in mind that for this check to be resisted, the target has to be actively trying to evade your drone. Being Surprised will certainly deny them this chance, and to remove the targeting once it's set, they will need to spend their action to sneak away from your drone. See this awesome video from Complex Action.
Rigger 5.0 adds the option to upgrade your Sensor array (p.123) for rating * 1,000 nuyen, or a single sensor for rating * 100 nuyen. This will replace the original sensor, so it will cost you 4,000 to upgrade from Sensor 3 (factory) to Sensor 4, 5,000 to Sensor 5 and 6,000 to Sensor 6, the maximum available.
About the Smartgun system
All drone-mounted weapons are "smart", you need the weapon to be connected to your drone hardware somehow, and you need software to be able to sense the targets, aim, and fire. But there are ways to make it "smarter", as shown by the Weapon Targeting program example:
[Weapon] Targeting: This is the Gunnery skill, but for a weapon of a specific model. If you mount an Ingram Smartgun, you’ll need an Ingram Smartgun Targeting autosoft for it.
The Ingram Smartgun comes with an integrated smartgun system, which will add +2 to its Accuracy (which is already high enough, depending on the weapon). But note that this will not add any dice from the Wireless bonus, as your drone neither has a Smartlink nor an augmentation that grants the benefits of it. So having a smartgun system is only going to benefit the rigger when jumped in.
However, Rigger 5.0 brings you the Smartsoft program (p.127), which is a rating 3 autosoft (1,500 nuyen) that allows all benefits of the smartgun system for drones. Install it and you can now benefit from +1 to your attacks.
If the weapon isn't smart already, like an Ares Predator is, you will have to either mount an external smartgun system (200 nuyen), or buy a version of that gun that has it integrated (twice the weapon's base price).
Disclaimer
As you might have noticed by now, this all costs a lot of nuyen. And even if you build the perfect combat machine, drones are still fairly fragile. Do you really want to have your drone attracting that much attention during missions? I would advise you against that, as not all contractors are willing to pay for your losses during a mission (if any of them are, actually).
You can easily build up a combat drone that costs up to the 70,000s and will still manage to get shot down by a lucky auto-fire's spray of bullets. For that much nuyen, you could have 4, maybe 5, smaller drones well-armed but rolling fewer dice on their attacks, which would still have a greater damage potential than a single heavier drone.
Best Answer
Is it too easy?
From your description he seems to be spending a large amount of his money on circumventing the possible consequences from his corporate SIN. Thing is, spending all that money to avoid the consequences is a consequence in itself.
How much time or money would a corp invest in tracking people with corporate SINs that aren't active employees?
The corporation should only care from a liability standpoint. They do not want their Corporate SIN associated with illegal activities that might damage their reputation and ultimately their bottom line. Its probably not feasible or cost effective that they would run heavy surveillance on the PC in question but more likely that a computer system would routinely screen and compare recorded behaviors (such as purchases, net activity, general location activity)behaviors against an algorithm that would flag the owner of the Corporate SIN as being suspicious.
Possibilities to make things more difficult but keep it fair
As you stated he's trying to maintain a cover, but what he does to maintain that cover is pretty pedestrian and anyone who examined his life closely if it all could see through it. Hint to the player (whether in game or out) that his PC's transaction history without any recorded income (and thus taxes for the Corporation which they do want) seems like it might attract attention. The PC then might have to build a real cover, a job with an income which pays taxes to the corp, a whole fake life including purchases, people who know him, an apartment (basically he would have to pay some part of a living expenses for the cover) which he will need to maintain. The corporation may send someone sniffing around after his previous irregular income and spending actions, but if he looks above aboard he may be able to ride it out.