There are a couple of limitations. One is that due to the low density of the Martian atmosphere (~1% of that at sea level on Earth), the area of the canopies has to be enormous to decelerate even a modest payload to a landing speed that is still several meters per second. With Pathfinder and the exploration rovers, this speed was dealt with by packaging them in protective balloons or (for Curiosity and the upcoming Perseverance) via a terminal retropropulsion system, a.k.a. the “Sky Crane”. Obviously a descent vehicle with a human payload would need to make a very soft landing for the safety and comfort of the crew. The other, more significant problem is that because the atmospheric pressure on Mars is so low, blunt (or bluff) body deceleration is not as effective as on Earth, and a parachute will be deployed while still at supersonic speeds at a very high dynamic pressure. This will impart a greater jerk and faster inflation than parachute deployment at lower (hopefully subsonic) speeds, and even using multiple reefing stages and dampening elements there is only so much that even a high tensile strength textile can absorb. Realistically, for a crewed Mars descent vehicle of 40+ metric tons, a combination of an inflatable decelerator like the LDSD and (possibly supersonic) retropropulsion will be required for a safe and controllable landing. Here is a brief presentation on the challenges of entry, descent, and landing (EDL) on Mars.
In theory you could do this but the reality is that the enthalpy of that reaction is so low and the molecular mass of the products is so high that the specific impulse just wouldn’t be good enough for a high thrust application. A lot of things burn, but very few things combust with enough energy and at high enough temperature to make effective chemical propellants, and the ideal propellant has products that are as low molecular mass as possible to increase the effective exhaust velocity. With LH2/LOx engines, they are often deliberately run hydrogen rich just to get better thermodynamic performance even though you are not getting complete combustion of the products.
As a first order estimate, you can look at the kinetic energy per unit mass of the orbit you want to achieve, from that figure out the Δv (change in velocity), estimate your inert mass (payload and launch vehicle structure and propulsion system), and use the Tsiolkovsky rocket equation to figure out the mass of fuel, assuming that you know the specific impulse of the propellant in the engine. You can even do this for multiple stages with different propellants just by sequential calculation. To account for drag and gravity launches for a ‘typical’ ground to orbit trajectory, multiply by somewhere between 1.10 and 1.15, depending on how fast your vehicle is. For a detailed estimate you would actually run something like the flight simulation you outline (which you’ll run anyway to assess vehicle stability and accuracy limits).
The main advantage of an air-deployed launch vehicle is that you can fly out to a location where you have your choice of azimuths and/or can launch into broad ocean area away from flight paths and commercial shipping lanes and thus avoid the necessity of range tracking or a certifying a sophisticated autonomous flight destruct system (AFDS). You can also fly above ground winds and low level weather systems that would halt a ground launch, but you can also be pushed out of your racetrack by even a hint of lightning or wind shear, so that’s a wash. Conventional air-launched vehicles are limited by the size of their carrier systems, generally something like a B-52 (first couple of Pegasus flights), L-1011 (subsequent flights of Pegasus and Pegasus XL), 747 (Virgin Orbit), or C-17 (pallet-dropped air-launched targets like SRALT, MRT, or LRALT). Stratolaunch Systems developed the worlds largest (by wingspan) carrier aircraft which was intended to carry medium-class payloads in a range comparable to Delta II but has yet to actually flight an orbital launch vehicle and they seem to currently be focusing on hypersonic test vehicles instead of orbital launch. As others have noted, the speed and altitude advantages are almost negligible while the complexity of air-dropping a launch vehicle is far from trivial even for a small satellite launcher, essentially combining the challenge of launching a rocket and flying very heavy external loads, plus a host of safety and monitoring issues.
Getting back to Mars, a sensible mission architecture would involve prepositioning an infrastructure, including supplies, habitation, power generation, and ascent vehicles prior to even embarking the crewed portion on an interplanetary jaunt versus the all-in-one approach of Apollo lunar missions. In that way you could at least verify that everything is working as expected, and you don’t have to coordinate a bunch of launches to bring all the mission elements together in one vehicle. But again, it would be better still to develop a more general infrastructure for space exploration first using autonomous systems to extract and refine resources so as to minimize the dependence to bring all resources from the surface of the Earth all the way to Mars. If you can find water ice in a convenient solar orbit, extract it using the reliable solar energy in space, and then send it down to the surface of Mars, you can afford to provide a large margin of resources versus being mass limited by sending everything in one or two shipments. Of course, building this kind of infrastructure isn’t cheap or easy, even compared to a single US$500B Mars crewed mission but it does create a more sustainable infrastructure for multiple missions and exploration beyond Mars. One less to be learned from Apollo is that when you program goal is to just get to a single destination, once you’ve achieved that you are done as far as politicians and the public at large are concerned. But if you have an existing infrastructure that makes subsequent missions so cheap that it isn’t worth arguing over, you can keep extending your missions indefinitely.
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