Alrighty then! I’ve got many questions to help me get started, and I hope all of you can answer them. All of them.
1. Why and how do I use 68k Asm on a z80 processing TI calc?
2. What is grayscale?
3. What is Axe?
4. What is the best operating system for games?
5. What do you recommend? AsmPrgm (Or whatever the function is that uses that. ) or z80?

1. You don't.
2. It's using gray colors instead of using monochrome ones.
3. A language.
4. The only one that really had any games: TIOS.
5. *sigh*

Can we start by asking better-structured, more specific questions? I'll be glad to answer things that are a bit less like "What is the meaning of life". Perhaps for your "What is Axe" question, you could ask something more along the terms of "What are the strengths/weakness es of the Axe Parser Programming Language? Where should I start with programming in it? Would you recommend it based on <insert your programming experience>".

Because I am really confused yet interested, let me get off to a better start. I understand my questions barely make any sense, and are difficult to answer.
So what ARE the advantages of Axe? Is it faster than Basic? Which language do you recommend for graphics? Can you incorporate different languages all together in any one shell?

1. You can't. You write z80 ASM on a z80 calculator, unless you want to write an emulator in z80 ASM that can run 68k ASM. However, because the 68k is a more powerful processor and 68k programs are usually much larger than the size of the z80 calculators' RAM, it would be an impractical project.

2. Grayscale (more shades of color on the LCD than just black and white) is created by blinking pixels on and off very fast. The most popular types are three-level (black, gray, white) and four-level (black, dark gray, light gray, white) grayscale. z80 ASM programs can easily use grayscale with Jim E's Grayscale Package, among others.

3. Axe is a compiled language, syntactically reminiscent of BASIC. It is considered by some to be a bridge between BASIC and z80 ASM as far as difficulty, but I don't personally recommend it if you're already working to learn the more powerful and efficient z80 ASM language.

4. Doors CS, of course! It offers tons of libraries for BASIC programmers, tons of libraries for ASM programs, and a huge list of features for users.

5. Those are the same thing. The hex codes that you enter for AsmPrgm are just z80 ASM mnemonic opcodes converted to their hexadecimal form. I recommend you write in mnemonics and compile with the Doors CS SDK.

Axe's advantages over TI Basic are that it's faster, easy to learn, and has more (gaming-oriented) features. However, it's also fairly limited compared to what you can do with pure z80 ASM. Doors CS can run nostub TIOS ASM, ION, MirageOS, and Doors CS ASM programs, along with TI BASIC with the third party libraries.

How is axe faster if it is syntactically similar to basic?

It compiles to z80 machine code, which is also what ASM assembles into. That said, while Axe may be faster for development, it produces unnecessarily large executable files and it's often much slower than hand-optimized ASM.

Well that helps! Thank you!

Axe _looks_ like TI Basic, but it differs in the coding style. For example, in TI Basic, you have all these rules about what gets stored in what variables (for instance, {1,2,3->A won't store a list to A, it will store a list to ListA). Axe also doesn't abstract you away from the memory. If you did {0}, it would give you the first byte of memory. Axe is fast because it's not an interpreted language (TI Basic has to read every single character, determine exactly what you mean by that, check the syntax, and then execute what you really meant to say), it's compiled, so all that checking is done at compile time and the program can stay fast.

Did we resolve this thread? I got the impressive that Dapiano was leaning towards trying out some good ol' z80 ASM first, based on our answers and our description of Axe, but are there any unanswered or follow-up questions to be addressed?