To answer various questions:
Biological weapons involve using low-mid level CHEMISTRY in combination with mid-level BIOLOGY.
Zombies require mid-level ECTOBIOLOGY and attaching a machine gun requires low-level KILLBOTICS
Mutated rats with shark heads requires mid-level BIOLOGY.
You'll start with low-mid level (level 3) of your primary discipline, low-level of a second one (level 2), and the books to utilize fundamentals (level 1) of two other fields when you have those books available.
KILLBOTICS:
KILLBOTICS rarely requires chemicals but demands a large number of parts, some of which are very hard to find. As you improve in KILLBOTICS, you'll need more complex workshops - beyond what other disciplines demand - to produce better and larger ones (or specialized smaller ones). A killbot can only be as good as the parts you make it from, no matter how good your PROGRAMMING science is. Speaking of PROGRAMMING, you have little choice but to make that your secondary or one of your books, because more complex behaviors, better success rates on your robots, and eventually true artificial intelligences require your to improve your PROGRAMMING skill in parallel with ROBOTICS. In addition, you'll have to outfit them with your own produced weaponry or buy weaponry off the black market, which can be expensive on top of the costs of specialized parts. Additionally, the few chemicals you do need will often be Volatiles, Purified Volatiles, and Purified Reactants for their engines/reactors. At low-level, killbots may be steam-powered (requires coal), gasoline-powered (four dollars a gallon, you poor bastard), or electric-powered (requires custom batteries - you'll get the battery design and parts/chemicals added to your INVENTIONS list if you choose this path.
The advantages are obvious - you can make durable extensions of yourself for no greater cost than what it takes to piece them together, equip them with anything you find, modify them on the fly, teach them to do anything, once you get the pieces, the KILLBOTICS skill to assemble them, and the PROGRAMMING skill to make them do what you need them to. Additionally, KILLBOTICS weapons are very adaptable over time - while authorities you anger may eventually adjust to, say, LAZORS with appropriate armoring, if the LAZORS on your killbots are no longer sufficient you may change them to missiles or bullets (or a combination thereof, if you have the CHEMISTRY and PHYSICS books/skills to make them yourself). This may even happen within a single confrontation if you have diversified your killbots' loadouts, and may happen without you even needing to order it with some simple weapon efficiency algorithms (PROGRAMMING level 3). Finally, robots become visually impressive quite rapidly, and are more likely to cause enemy forces' morale to collapse at early levels, while not losing their impressiveness over time like many other forms of SCIENCE! do.
Feel free to ask about any other forms of SCIENCE! you wish to know about.