The locks on my house are fire-safe in that a person on the inside can let themselves out without a key.
What type of locks did the Gemara have in mind, that a parent is liable if he didn't lock his young child in the house and something happened to an item being watched?
There was an earlier discussion in the gemara about a gate, perhaps to the Beis HaMikdash, where one had to inser their arm in fully around a bend in order for the key to reach the lock, and if a professional gate openner dropped the key, they would have a liability.
Again, what types of locks did they have in the time of the Gemara?
Without going into what kind of locks they had in the time of the Gemara, we can deduce the guideline to the amount of guarding necessary from Rashi's comment. Rashi (DH "b'Fneihem") says "(And he locked) in front of those children in order that they should not go outside and lose the money." This apparently means that any lock which would enable the children to go outside, including a a fire-safe lock, would not be considered proper protection for the money being watched (assuming the kids involved are old enough to access the fire-safe lock). If he is concerned about the fire hazard, he should not leave his young children alone with his friend's cash (unless it is in a safe), or not agree to watch the money.
All the best,