A traveller praying with local residents

A traveller arrived [in town] and found the [local] people praying [the] ‘asr [prayer]; they had [already] prayed two rak’ahs, [so] he joined them for the [final] two rak’ahs. [Considering he is a traveller, should he suffice with just praying these two rak’ahs with them or] should he complete the prayer [by praying all four rak’ahs]?

Traveller returned home in Ramadhaan during the day and wants to have sexual intercourse with wife

A man returned home from a journey and had not been fasting [due to his travels, so he] decided [now he was at home] to fast [the rest of the remaining day]. He then found his wife taking a bath [since she had] completed her menses; Is it permissible for him to have sexual intercourse with her in this case or should they both assume the fast for the [remainder of the] day?