As said before, there is no such thing as "invisible" on the Internet, short of not being connected at all. But there is a gray scale of "protection layers" of setting blockages for certain network traffic, depending on how you want your host to handle it. I'.e., like the rules you showed on top, which indeed tells the host to drop certain incoming ICMP packets, rather than deliver them to their normal handling (by the kernel). I think you'd do well in dropping IGMP as well, and then consider blocks for TCP and UDP messaging, which offer the majority of intentionally harmful networking.

If your computer 'reaches out' via some other port, then it won't be entirely invisible, likewise if there are any ports that are open or explicitly give rejection messages (as opposed to simply dropping them).

If you want to determine how 'quiet' your machine is, from an external machine (there are some limited capacity sites that offer this) you will want to try to use nmap to do a full blown port scan coupled with an OS detection attempt on your given external IP.

If nmap detects any services, ports in use, or is able to guess it's OS (with reasonable accuracy), then it's not 'quiet' (I use 'quiet' to distinguish from 'invisible' because nothing is truly invisible, even airgapped networks can be penetrated). Naturally, if you connect to any web service then that service knows you're active. Even if your system is 'quiet' a Trojan or backdoor could still 'leak' information out.

It's also worth noting that even if your own machine is 'quiet', your router might not be.

Regardless, it's a good idea to keep the ping reply 'quiet' on a system, because part of avoiding an attack is not letting an attacker know there is something there to be attacked.