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So, the white piece has identification, but the front cover does not. How are these identified? It's from an old space set from the 90's. I have tons of non typical parts that seem to have no identification. It does have some numbers on it - 1-02 what is that referencing? I know this was from a few sets, probably
The box is part 4345 (or a variant). On BrickLink, that gives This Door, Frame fits with the following Door:. And those parts are 4346. But you want one with a pattern on it, so the BrickLink search you need is 4346p*. There's only 60 of them, and one looks right: 4346pb05 Container, Box 2 x 2 x 2 Door with Slot with Red and Yellow Controls Pattern
As for "1-02 what is that referencing" it is almost definitely a way for Lego to track which part of which mold made that part, so that if any are reported as mis-formed, they can track it down more easily.
These parts are Tile 1 x 2 with Groove with Red and Yellow Controls and Two White Stripes on Left Pattern,
Note the similarity to this part (below). You can see the left side is different.
Container, Box 2 x 2 x 2 Door with Slot with Red and Yellow Controls Pattern, attached to Container, Box 2 x 2 x 2
As for finding pieces yourself, I find the Bricklink search to be most useful. Obviously as you become more familiar it will be easier. Searching by colour is usually a good way to start.
To find your parts I searched "white tile 1 x 2 pattern red yellow" and "black container door"
