Q:

Are packets processed by a proxy new or modified?

Client ---> First packet ---> Proxy ---> New packet? ---> Server 

If we speak about proxy systems, does the first packet get discarded and a new packet gets created, or it's still the same packet (TTL gets decreased) any only the Layer 2 addressing gets changed? So if the L2 addressing gets changed do we speak about a new "packet"/"frame"? What if SSL/TLS is involved?

A:

When using a proxy there is one connection between client and proxy and another connection between proxy and server. These connections are usually fully independent regarding TTL, TCP flow control, packet size (when using TCP) etc. Often they also have different source and destination IP and ports, i.e. with an explicit proxy the target of the connection from the server is the proxy, the target of the connection to the server is the server (different from proxy) and the source of this connection is the proxy (and not the client). Even the application layer content might be different, for example by injecting X-Forwarded-For headers into the original HTTP request when forwarding the request or Via headers into request and response.
Some proxies explicitly extract packet layer information from the source connection and apply these to the target connection when forwarding the data. Often this is the destination IP address when the proxy is configured to be used in a destination transparent way. It could also be source IP (and port) if the proxy is used in a fully transparent way (destination and source transparency). It might in theory also be possible to extract the original TTL and apply it when forwarding  but I'm not aware of any proxy doing this.
With SSL/TLS involved the situation is no different. If SSL interception is done then there is one SSL connection from client to proxy and another one from proxy to server so that the proxy can get the plain text data. If no SSL interception is done then there are still two TCP connections but the proxy will forward the encrypted data directly.
Note that the behavior of a proxy as used in an application layer gateway as described above is different from Deep Packet Inspection (DPI) as done in many Next Generation Firewalls (but not all, some employ proxies). With DPI the original packet gets forwarded which includes the same source and IP address and port and also TTL. SSL interception is not possible this way, i.e. for this the firewalls also employ (transparent) proxy technologies with one SSL connection between client and firewall and another one between firewall and server.

