Between the rules and the card descriptions, I am not sure I understand this rule:

For a Play-on-the-table Kingdom card, does the attribute last through a whole seige/battle or just one die roll of a seige/battle?

For example in a player-on-player battle (contest) does the Bossonian Archers card noted on page 22 of the rules, last for one die roll of a contest or for all die rolls of one contest? Just a couple more words added to this rule would positively nail down the rule meaning. (Related: I am not sure if a Battle is defined as one contest or a series of contests.)

Just a single roll of the dice. It you continue on with a forced march, or another round of combat, those effects are gone.

Indeed. Those bonuses afect only one combat (one roll - with rerolls). After that when you force-march then it's a whole new combat with new bonuses. The same thing applies to Strategy Cards - they last just one combat.