Logic gates question?

You are missing a lot.

First of all, the output of a gate has to have more voltage and more current than the inputs or else the output cannot drive a second gate's input.  In the real world, it has to drive at least 4 inputs. This is called the Fan-out. Your example and the one you reference have fan-out's of less than 1.

Second, the two inputs should be identical in usage, to make the gate easier to use.

Third, a transistor costs almost nothing.  

Actually, the drawings you reference are not a type of gate you can use, they are too poor in performance for that. For example, the voltage output on a high input is lower than the input voltage, so they do not meet the first criteria listed above.

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NO you cannot. An AND gate has 2-inputs and a transistor has only one.
If you examine the circuit you will see that there are (2) transistors to isolate each input.
You can also accomplish this with diodes that are reverse biased (operate in off mode pulled to ground).

The way you described it is not an AND gate, but what is called a DRIVER or INVERTER with an ENABLE.
You are using the base to ENABLE the collector to pass. You are not logically ANDing the two.

Examine the logic truth table and run thru all possible combinations and you will see that if B is true that A will pass thru and potentially change the output. This is an unstable conditon and is NOT true for every possible case.

The logic functions must be able to pass all conditions for all states of electricity not just logic !!

Also for an Emitter Coupled Logic Output, this is a HIGH CURRENT logic for FAST SPEED and is again a form of OUTPUT ENABLE not logic !! Read the power supplies section of this logic carefully:
http://en.wikipedia.org/wiki/Emitter_coupled_logic

This is a speed advantage as is schottky logic:
http://en.wikipedia.org/wiki/Schottky_transistor

Take it on faith that transistor logic was simplified years ago. When i was you age i wanted to create a 3-state logic that i later found out to be what is tri-state logic. Today there are many types of logic including Fuzzy Logic, which never really caught on either.

There are new forms of logic prediction methods that you may want to look into. This will likely form the basis of articial intelligence.

Good luck young feller !! You are the only hope future of tomorrow !!