There are many different and equally valid answers to those questions.
If you simply wish to create a limited adventure that uses a simple verb-noun input then check out one of the books that detail the development of such a game from beginning to end. Archive.org hosts some good ones.
Such as:
1) "Commodore 64 Adventures: A Guide To Playing And Writing Adventures" (Mike Grace, 1983, Sunshine Books, ISBN 0946408114)
Read online.
2) "Adventure Gamewriter's Handbook" from Abacus.
Read online
Download the game system
3) "Creating Adventure Games On Your Computer" (Tim Hartnell, 1983)
As you can see, should you peruse them online, implementations vary. But generally the implementation accommodates the BASIC 2.0 language rather than use BASIC to simulate non-native (and more useful) processes and data structures. Despite this, these books from the 1980s are still useful for exploring BASIC implementation and game design.
IMO, a modern adventure game engine, written in BASIC 2.0 would be one based on the Inform system - declarative, object-oriented and event-driven. Writing an engine based on those concepts, cut-down for BASIC 2.0, in 64K at 1Mhz, would be a challenging, non-trivial exercise.
1. How do you define rooms with objects in them? and a player?
2. How do you define multiple possible inputs, each with their own response?
3. Do you have the source code to a game that you programmed? If so could you post it?
1. Perhaps use a 2-dimensional array. The first subscript would indicate the room, the second subscript the room's object. The object's unique ID (an index) would be stored in the array. The object index could then be used to access the item's properties (name, type, etc) which would be stored in other arrays.
The player? Define his inventory as an array and store object IDs in it. Have another array for state information such as location index.
2. There are many ways. Some are elegant, others ugly.
A simple method might use an encoded format that encapsulated the basic rules of each possible action. If the rules were read from DATA statements they could be processed a bit before being stuffed into arrays. But it would still be an ugly brute-force approach. Fortunately, the books listed above have some better ideas.
3. Nope.
Oh and how do you change variables to equal something else later on?
Use the assignment operator, "=". As in
10 A$="red"
Fundamentals for BASIC programming can be found in the
Users' Guide.
Go to chapter 4.5: How To Use Variables.
Everything you do towards the goal of writing an adventure program needs to be ordered so that each step is built upon its predecessors. If you skip something, then you'll stall. Once you understand the BASIC language you'll be able to combine that knowledge with imagination and creativity to develop solutions.