Basic questions on how asymmetric keys "interact"

Question

Have I understood this correctly?

1. To use a key and lock analogy. With an asymmetric pair of keys (when used to encode) can either key be used to encode the message (close the lock) and only the "pair" be used to decode (open the lock)?

2. Taking the key analogy further, is it a useful comparison to say that the first key of the pair changes the lock after it is used so that only the "not yet used" key of the asymmetric pair can open the lock?

3. The description of keys as "public" and "private" is only a convention that relates to their use and not the order in which they are used i.e. can use 3.1 public then private (encoding for one intended recipient) or 3.2 private then public (digital signatures)?

Edit: Wording of point 2 altered following comment by Maarten Bodewes.

Answer 1

To use a key and lock analogy. With an asymmetric pair of keys (when used to encode) can either key be used to encode the message (close the lock) and only the "pair" be used to decode (open the lock)?

No, not in practice. Although some systems work kind-off like that, for instance raw (unpadded) RSA, others do not. Besides that, one key is supposed to be public so anybody could use that key to open the lock. Locks are used to emulate encryption, and encryption is used for confidentiality. If you use the private key to lock then anybody could open the lock. That's not a good way to achieve confidentiality.

The confusion mainly seems to arise from RSA where signature schemes were seen as encrypting a (padded) hash value. Nowadays the specification of secure RSA goes out of the way to make sure this confusion doesn't arise. More information here.

Taking the key analogy further, is it a useful comparison to say that the first key of the pair changes the lock after it is used so that only the asymmetric key of the pair can open the lock?

Both keys in the key pair are asymmetric to each other. So there is not one asymmetric key, but two (or more). The analogy is already broken, it doesn't make sense to take it further.

The description of keys as "public" and "private" is only a convention that relates to their use and not the order in which they are used i.e. can use 3.1 public then private (encoding for one intended recipient) or 3.2 private then public (digital signatures)?

Yes, that is right.