An old tomb is an ancient tomb. They're mostly from the Kofun period, and indeed that's where the period gets its name.
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
The number of people visiting the ancient tomb has been increasing in recent years.
In this cafe, you can eat cakes in the shape of ancient tombs.
Furukawa-kun is ancient tomb enthusiast.
The Kofun period refers to the period from around the end of the 3rd century to the 7th century.