Almost impossible to answer without knowing what pre-emergence you are using. Some only last a month or two, while others can last up to six months.

Pulling weeds is a periodic but constant chore. You're never finished, and there's no product or method you can use to stop them permanently. If there was, we'd all have/use it & there would be no weeds (and the inventor would be the richest person - ever!) When you see something sprouting, pull it out before it becomes difficult to do so. When you are walking around, looking at your lovely yard, pull them when you see them. Don't wait until you 'have weeding to do.' That's no fun & a lot more time consuming. Yes, I would start with a clean slate by pulling them now. This is the time of year I can see little tree sprouts hidden by foliage during summer. A weed-wacker/trimmer should be able to help you keep the lawn from being able to climb into raised box/beds. Maybe I'm not imagining your situation correctly? Feel free to add a pic to get the most specific suggestions.

Second one looks like a salvia of somekind. Can't tell what the first is maybe someone else can help out.

I thought you decided it was Ageratina altissima. If so, it's a native.