Weeds can grow through rubber mulch, but it depends on if you removed all the weeds in your garden beforehand. Weeds already in the soil can grow even when using rubber mulch. However, that doesn’t mean that your garden will be littered with rubber and weeds, but it does mean that the occasional weed might still pop up. Another way you can increase your weed suppression is by using landscape fabric as a second layer. 

No, it's not really possible to completely prevent weed growth. Weeds are incredibly resilient—all they usually need is a tiny bit of dirt to sprout, so their eventual appearance is pretty much inevitable. However, you can definitely keep them at bay by getting rid of weeds as soon as you notice them. The longer you let them sit and grow roots, the more they'll spread.

Crabgrass is very resilient, and homemade solutions like vinegar may not be strong enough. Typically, hand-weeding is the most effective option that doesn’t involve harmful chemicals. You can use corn-meal gluten as a natural pre-emergent herbicide, but it’s not as effective as chemical weed killers.

There are many options to eradicate weeds right down to the roots. Vinegar works, but it takes a week or so to do its thing, and the same goes for many commercially available herbicides. Boiled water is a quick way to kill off roots, or you can pull up weeds at the root.