Intercourse entails ritual impurity. One can not perform prayers(Salah) or visit a Mosque while in a state of ritual impurity, and everything else is permissible. Ritual impurity caused by intercourse is removed by performing Ghusl(bath) See IslamQA.
Regarding eating, it is not necessary to perform Ghusl before that, though majority opinion is that it is considered mukruh(disliked) to sleep without performing Wuzu(ablution) and to eat without washing the hands ... though there are some conflicting Hadith on the matter.
Whenever the Prophet (ﷺ) intended to sleep while he was Junub, he used
to wash his private parts and perform ablution like that for the
prayer Saheeh Bukhari
'A'isha reported: Whenever the Messenger of Allah (ﷺ) had sexual
intercourse and intended to eat or sleep, he performed the ablution of
prayer. Sahih Muslim
It was narrated from 'Aishah that if the Messenger of Allah (ﷺ) wanted
to sleep while he was Junub, he would perform Wudu', and if he wanted
to eat he would wash his hands. Sunan Nisai
One can perform intercourse multiple times and bath only once after that. In common practice intercourse is performed at night after the last prayers of the day(Isha) and before the first prayers of the next day(Fajr), and a bath is taken before the Fajr prayers. The other common practice is to perform it in the afternoon between the Zuhr and Asr prayers, and to perform a bath before the Asr prayers. Normally its not a custom to eat at these times. Daily morning and occasional evening showers are usually taken even if intercourse is not performed, for general hygiene purposes, so it blends in ... otherwise Muslim families are usually understanding and respectful about the matter.
