At the start of the year re-edge your lawns with a half moon edging tool. Use string to get straight lines. You'll find it hard work but gives your lawn a great start.
Mow frequently during the growing season. This keeps weeds under control and encourages the lawn to grow.
Feed regularly
Trim edges with edging shears each time you mow. If you don't like this
job then put paths level so you can simply mow the edges.
With wonky edges you might find it easier to repair the edge by cutting a square out and turning it around so you get a straight edge.
Dealing with walked on lawn - if there's a natural path being worn through your lawn the easiest thing to do is to stop fighting and let there be a path there. Put a path down of gravel edged with wood, or stone flags or concrete slabs.
Spend an hour taking out any dandelions. Use a grubber or a long knife to slice them out deeply at the root.
If your lawn is uneven you can level small dips out using a sliced H shape and then peeling out from the middle crossbar and putting soil underneath, and replacing the lawn. Water well.