#1 May we use tools to increase/change results of a card?Yes - but only when the rules say so.
That would be the cards where you roll two dice to get a specific type of resource. The 'Gift cards' where you roll a die per player will yield a specific set of gifts that cannot be changed.
#2 Do we have to anounce if we are going to use tools BEFORE rolling the dice or may we add tools only after and if needed?No, you may decide to use any number of tools or not AFTER having seen the outcome.
#2.1 And may we transport any not used part of a tool to use on another die roll result? (eg. suposing that I've just used 2 pips of a 3 tool)No. The rules clearly state that any given tool tile can only be added to a single roll.
#3 If the card display is empty do we add the number of cards equal to the number of players or do we always replenish the display with four cards?
There should always be exactly four cards in the display at the beginning of each round. Cards are only removed when bought, any unbought cards are slided to the right (towards the cheapest price) before filling in the empty (more expensive) slots.