Learn Portuguese (Portugal): Li o manual e guardei na gaveta. - I read the manual and put it in the drawer.

This sentence uses the inanimate null object. In European Portuguese, when a direct object refers to a lifeless thing like o manual and was just mentioned, you can completely drop the pronoun. While guardei-o is also correct, simply saying guardei is very natural and common in everyday Portuguese.

Can I use the verbs pôr or colocar instead of guardar here?

You could, but guardar carries a specific meaning of putting something away for storage or safekeeping. While pôr or colocar just mean to place an object somewhere, guardar na gaveta implies you are properly storing the manual in the drawer so it doesn't get lost.

Could I use the Imperfeito tense for these verbs if I was setting a scene?

Only if you wanted to express a repeated past habit, like saying you used to read the manual and put it in the drawer every day (lia o manual e guardava). Since this sentence describes a sequence of two completed, one-time actions in the past, the Pretérito Perfeito (li, guardei) is required.

Why isn't the subject eu used before either verb?