Check some sentences please

Hi. Please help.

1. Is the use of the modal verb "would" a past of the modal "will"? The fact (part?) that is confusing me is that without further context, by the underlined sentence alone, I think the sentence would be thought of as a conditional sentence (in the present).

They took notes. For them, writing things down on paper would give them something tangible to keep for many years.

2. Would you say the preposition "on" in optional here?

You have an end room on the floor so there is no one (on?) the other side.

3. I think the two sentences are different in meaning. I think the second latter sentence focuses on duration of his playing with the YYY more than the first one.

He played basketball for the XXX for three years, ending in 19XX, and two years before that (could it be this, too? two years previous to that), he was with the YYY playing center.

He played basketball for the XXX for three years, ending in 19XX, and for the past two years before that (could it be this, too? for the two years previous to that), he was with the YYY playing center. -- Here, I don't think we can use "for the last two years before that." Right?