Do the Orthodox make and use makeshift altars when they need to celebrate the Liturgy in secret?
First I should point out that in the Eastern tradition one person can not celebrate the Liturgy there need to be multiple people present. We would never call it a secret liturgy since anyone from the faithful would be welcome to it.
The eastern tradition also has something called an Antiminsion which must be used for every liturgy and in reality it is a portable altar. By placing the Antiminsion on a table it becomes an altar. The Antiminsion is a miniature version of the epathasios that is used during Holy Week and is placed on the altar from Pascha until Pentecost. The Antiminsion consist of an icon of Christ in the Tomb and has the signature of the Bishop.