He offer to do that for me without my request.

我没提出要求。他就为我去做了那件事。

Jack, I appreciate your offer to do the dishes.

杰克，你要帮我洗碗，我非常感谢。

Is there something valuable they offer to do for them in exchange?

他为换取他所需要的而提供的东西是否有价值？

Offer to do their flight reconfirmation, changes or new bookings.

为客人提供机票确认，更改或预订机票的服务。

Offer to do so at a low price in order to establish some credibility.

开始时开价要低，以便建立好信誉。