The absolution you receive in the confessional forgives all of your sins unless you or the priest have done something to invalidate it. The penance you’re given simply completes the process and helps to remit some of the temporal punishment that you have to pay off.
If you honestly forgot to do your penance, you are bound to do it once/if you remember it. If you can’t remember what it was, you can simply pick any suitable penance yourself (emphasis on the “suitable”).
But intentionally avoiding it is another matter. If you go into the confessional with no intention of doing the penance assigned to you, that would constitute insufficient contrition and would invalidate your confession. If you confess intending to do the penance you’re given but then refuse to do it later, you would be guilty of grave sin but your confession would still have been valid. The priest is also bound to give you a proper penance, but it’s not a good idea to judge the suitability of your penances unless what he tells you to do is truly rediculous.
In regards to the “more specific” penances, the ones you cited are things you would be bound by justice to do anyway (in most cases). They really aren’t appropriate penances for an adult, so if you’re told to do something along those lines I would think it would be just as a reminder of what you’re already required to do.