Have you considered getting rid of death?

Hi! Biologist (kind of, Biotechnologist and PhD in Bioinformatics) here. 

Biology as a field is way too broad.  You can pick any branch of biology and spend your whole life studying that, there will still be things to learn.  Having said that, and given that you're interested in things related to longevity, I would:

1. First, be aware of one thing: there is a massive difference between Biology and Physics ( I could make a similar comparison with other sciences, but Physics serves my purpose). Feynman explains that VERY well in his book "Surely you are joking Mr Feynman". Physics students try to develop an intuition about how different models of the world work. Biologists, on the other hand, f**ng adore memorizing names by heart and many old University professors think that it is the right thing to do (e.g. memorizing the names of the molecules involved in the Krebbs cycle).  The result is that most things that Biologists studied at some point are simply forgotten. For instance, I studied a few courses on Plant physiology but if you ask me what is the difference between C3 and C4 plants I have no clue.  So my first piece of advice is, "try to learn Biology as a physicist would do it". Learn the important concepts and learn how to reason about those concepts
2. Second, develop a solid understanding of Molecular Biology.  I would buy (or borrow) "Molecular Biology of the Cell"  aka "The Albert" and read a few chapters. The concepts you should be very familiar with are:
   1. Replication, transcription, translation
   2. The basics of genetic regulation
   3. Metabolism, especially how the cell obtains energy: respiratory chains,  ATP synthesis, etc. 
3. YouTube is your friend. There are very good channels out there explaining complex concepts.
4. Some of the names of molecules and metabolic pathways will be unavoidable important, e.g. caspases. Use Anki to memorize those. This might contradict a bit the first point, but you will need to develop some "general culture" and this requires memorization.  For instance, words you need to be familiar with: respiratory complex system, NADH, telomeres. Words you do NOT be familiar with e.g. Succinate Coenzyme Q Reductase. 
5. Try to explain the different things that you learn without using their real names.  E.g. can you find an alternative name for every part of the machinery involved in ATP synthesis?  (for example, instead of saying ATP synthase, you could say nano rotor that puts together ADP and P). If you can do that for most things that you learn, you are good to go. 
6. Read "Power, sex, suicide". It is a popular science book but it has a very good level. If you have spent a few weeks/months reading The Albert, you will understand most of it.
7. In Biology Evolution is King.  You don't need to understand the in and outs of population genetics, but you certainly benefit from understanding what we know about the origins of mitochondria for instance. 
8. Speak with biologists and test your ideas with them (in the best case scenario, find people having PhDs). Say to them you think "that we could just do some engineering in the telomerase" and we would solve the longevity problem. Some of them might not follow what you are saying. Search for the person that laughs at this statement and tell him/her to explain why this wouldn't work. That's the guy you want to hang out with. Speak with him and make him ridicule your ideas. If you understand why the things you are proposing do not make sense, this will mean you are learning.

My suggestion is to pick a specific aging research question and dig into the models, methods and evidence. For example, when people hypothesize that “naked mole rats don’t age,” how do scientists study that hypothesis? How does that inform our concept of “immortality,” and what is the distinction between “being immortal” and “not aging?”

I think you’ll have better luck with this approach than trying to build a very broad, somewhat undirected knowledge of biology. Nothing wrong with broad knowledge, it’s just that only a tiny fraction will be directly pertinent to any particular topic you’re interested in.

I have a reading list and recommendations for sources of ongoing news in the longevity/immortality/life extension space in the show notes for the recent special episode of my podcast where my co-host Michael and I discuss ageing and immortality. We are both biology PhDs, my background is in the epigenetics of ageing and Michael's bone stem cells.

https://www.xenothesis.com/53_xenogenesis_ageing_and_immortality_special/

I should add "Immune: a Journey into the Mysterious System that Keeps You Alive" to that list actually.

In particular from that list I recommend these for 'coming at biology from a physics perspective':

• Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies by Geoffrey B. West https://www.goodreads.com/book/show/31670196-scale
• life’s ratchet Life’s Ratchet: How Molecular Machines Extract Order from Chaos by Peter M. Hoffmann https://www.goodreads.com/book/show/16691583-life-s-ratchet
• Every Life is on Fire: How Thermodynamics Explains the Origins of Living Things by Jeremy England https://www.goodreads.com/book/show/50358530-every-life-is-on-fire

I think the Peter Attia Podcast is a good source for informationen on research about moderate life span extention. https://peterattiamd.com/podcast/

Learning biology is hard because biological systems are very complex. Given that complexity, biologists are generally happy to search keys under streetlights. 

A lot of the important arguments when it comes to longevity are about making guesses about the territory that's not under the streetlights. The knowledge we have about biology is already quite large, but it's important to always keep in mind that it's far of from being complete.

While learning biology your task is to both learn basic concepts to make sense of other knowledge and also learn about the system of how the knowledge gets produced. 

In Core Pathways of Aging [LW · GW],  John Wentworth for example makes claims about many people in the field approaching the subject wrong. You want to understand claims like that about the nature of the information landscape. 

One aspect of the article is that he talks about transposons as potentially being a very important part of aging. DNA sequencing that can only look at short reads like Ilumnia sequencing, can't tell you how much transposons doublicated. Given that the subject was hard to study, biologist essentially proclaimed that the existing transposons in the human genome don't do much. 

I am an undergraduate studying chemical engineering, and I've been intending to dive into learning about biology relevant to aging for about a year and a half, with relatively slow progress. I'd be interested in developing a rough schedule of things to learn about alongside you if you're interested.

I'd recommend checking out Laura Deming's blog, which has a list of things to learn about to get familiar with our current understanding of aging.