There is typically no need to replace your sim card unless you are having problems with it (ie not registering on the network.)
However older sim cards have a restriction on how many times they can register on the network, and after they hit the limit the phone will stop connecting, so if you want to prevent this issue (usually takes a couple years, and is a lot more likely in areas where your signal drops, for people who travel a lot, and in 3G coverages areas where you swap back and forth between 3G and 2G) you can use one of the newer sim cards. To Identify whether your sim is the newer variant with no registration restriction look at the back where the gold contacts are, if its a newer sim it will say in small lettering "TMXXXX" (where X is a number, ie TM4322) and it will also have an expiration date printed (it must be activated by this date or it becomes unusable.)
In terms of 2G/3G the sim card itself and its age should not make a difference as the capability to connect to those networks is dependent on the phone, not the sim. You can think of a sim card as a gateway that connects your phone to the billing system and authenticates it.
Having had said that, if you are having connection issues it could just be a defective sim card, to check, just place the sim in a phone that isn't having any connectivity problems, if it starts having problems, replace your sim.
In terms of the digit you highlighted in that picture, I believe it has to do with the manufacture year, although if I remember correctly its digits 4 and 5 that make up that information, but otherwise isn't anything important to a consumer.