1. Most of the "weeds" that are growing in that mulched area may well be growing in the mulch, something that happens when the material is not periodically renewed, and can easily be pulled out, or killed simply be stirring the mulch material with a cultivator. However the "landscape fabric" can be removed, if desired, simply by carefully lifting it up and out and then replacing the mulch that was there.
2. You can aid in "weed" suppression, after removing the fabric, by laying down newspaper and covering that with a mulch material. That will also help suppress "weed" growth in the future, but there is nothing that will prevent "weeds" from growing if they have half a chance. Since Ma Nature does not like here soil left bare she grows what we call "weeds" to try to protect that soil fromt he ravages of the sun, wind, and rain. When we put down a mulch, thick enough to protect the soil, then those "weeds" will not grow.
3. You can work at digging out those "weeds" or you can lay down newspaper over them and cover that newspaper with a good mulch material and that can help suppress those "weeds".
Be carefull with boiling water because that can also harm your wanted plants.
Never, ever apologize for asking a question because that is how you learn.